If we use gradient run in order to separate high-polarity range multi-components and mid-strength of mobile phase as solvent, what should we do to avoid precipitation of very-nonpolar components in first time condition (polar) of mobile phase of gradient system.

As a general rule, it's inadvisable to dissolve your sample in a solvent substantially more "potent" then your initial mobile phase conditions. If you follow this rule, you won't have to worry about precipitation and you're chromatography for early eluting compounds will be much better. Often it appears that it's necessary to use low polarity solvent systems to dissolve the sample in one step but this can be avoided by first dissolving the sample in a low polarity solvent and then diluting it in water, making sure that all components stay in solution. Otherwise, another option is to minimize the injection volume to overcome this problem.

Another approach is to use DMSO (it is not strong solvent in LC terms) as a sample diluent. It will keep your hydrophobic and hydrophilic compounds in the solution long enough to reach the column. DMSO is UV active, but does not retain on RP column. Expect to have DMSO peak in void.
Still another approach is to use mixed-mode column to retain polar and non polar components at isocratic or shallow gradient conditions with high organic concentration. If polar compounds are ionizable then they can be retain primarily by ion-exchange mechanism (even at high organic) but hydrophobic compounds will retain by RP mechanism.
See example
http://allsep.com/makeChr.php?chr=Chr_037 for retention of polar acidic and hydrophobic compounds at isocratic conditions and http://allsep.com/makeChr.php?chr=Chr_035 for retention of polar basic and hydrophobic compounds at isocratic conditions with 40% MeCN.

Why do you worry about precipitation in the inital mobile phase conditions? Don't you want these compounds to stay on your column?

If compound precipitate too early, means before it adsorbs on a stationary phase, it produce disturbed peak even in gradient mode. Reason for that I think (I never study it though) formation of small particles of the non soluble phase with dimensions bigger than pore size of the stationary support, but smaller than packing particle size (between 0.1-5 um on a typical column). Those particles will spread along the column, because of size exclusion.
By the way, sometimes you need just a small amount of DMSO in the sample to eliminate this problem not necessary pure DMSO as I said before.

For analytical separations, I agree with Chris. In most cases the best approach is to dissolve the sample in the starting conditions of the buffer. Then there will be no precipitation, and nothing to worry about.
If this is not possible, for whatever reason, and you need to dissolve the sample in a higher organic composition, you are likely to get peak distortions, unless you use a small injection volume. The peak distortion will happen for the peaks that elute early in the gradient, i.e. the polar compounds, and the hydrophobic compounds will be unaffected. Thus the precipitation is not the problem, but the solvent strength.
Unless the concetration of the hydrophobic compounds is very high, I would not worry about it at all.
I also disagree with Zelechonok that precipitation causes a peak distortion. We have used precipitation techniques in preparative chromatography to get around peak shape problems. Published in the Chromatographia Supplement Vol 57, 2003, S121-126. This is the opposite of what he says.
DMSO can be problematic. It can carry analytes through the column unretained, while still showing rather normal peaks for the part of the analyte that is retained. I know that DMSO is used a lot, but it often creates more problems than it solves. Specifically for preparative chromatography, we have used the at-column dilution technique to get around the problems caused by DMSO (see the article above).

I am disagreeing with Uwe Neue. In my 10 years of using DMSO as co-solvent in analytical analysis I never saw DMSO carries analytes through the column unretained. What is true for prep separation is not necessary true for analytical one where ratio of analyte to the stationary phase is 100 times lower. And again precipitation technique can work in prep and does not work in analytical since criteria of a good separation in both cases are significantly different.

Well, Zelechonok, the carrying through of analytes with DMSO was not a prep exercise, but an analytical separation. You need an MS though to see it, or even become aware of it.

The point of the discussion was initally, if one should worry about precipitation in analytical chromatography. Unless the material that precipitates is there in a large abundance (e.g. proteins in a plasma sample or in milk), precipitation is not a problem. I like the statement of A.Mouse: after all, you want the compounds to stay on the column.

Uwe Neue, let me to disagree with you again. In analytical chromatography you goal is not somehow precipitate compounds on a column. What you really want, unless we talking about different chromatographies, to form a narrow band of the compound on a column and elute it as a symmetrical peak with high efficiency. Quite often, when compound precipitate you would have disturbed peak.
I am not questioning situation of polar poorly retained compounds carried through the column with DMSO containing sample probe (you don’t need MS to observe it, DAD is good enough in many cases), but if a compound precipitates from the mobile phase because it is very hydrophobic the addition of DMSO would not make situation worse. As you said before people used DMSO a lot. Apparently not for the purpose of creating problems.
Let’s the syx_interbat check the situation with a simple experiment.

To go back to the original question, it should be pointed out that the sample, by in large, stays in its solvent for some finit time after injection and will reach the head of the column still associated with some concentration of original solvent, which may prevent precipitation. Once at the column, then the analyte has the opportunity to partition (dissolve in) the stationary phase as an alternate to precipitating.

If the sample were to precipitate, it could be a problem as the kinetics of these particles dissolving in the stationary phase would likely be unfavorable and therefore result in peak broadening unless the particles were large enough to filter out.

I used DMSO as a solent for lots of things. It is great for mixes of polar and nonpolar stuff. Shoot 5 or 10 uL samples and no problem.

I guess I started this discussion by asking why one should worry about precipitation. If the quantities are small enough they will not cause a plugging of the column. I also agree with Bill, that a small injection volume of DMSO is not a problem, since in most cases it is diluted enough by the time it reaches the column to not cause any peak distortion.
I do not understand the argument by Selechonok. On one hand, you are saying that precipitation is a problem, on the other hand, you advocate injecting the sample in DMSO, which may create a precipitation on the column. What is your point?

To A.Mouze.
Some how you manage to miss my point. I will try again!
You have to distinguish adsorption from precipitation. Adsorption is good. Precipitation is bad. Adsorption occurs on a surface of the stationary phase. Precipitation occurs in the volume of the liquid phase. When precipitation happens before adsorption you may observe peak distortion. DMSO can keep analytes in the solution till they get adsorbed on the stationary phase. DMSO as a polar compound usually washes away in pre-void volume and does not participate in the separation.

To A.Mouze
With small injection volume one needs to worry about precipitation because of peak distortion not because of plugging. Earlier I tried to explain why the peak distortion happens.

Does anybody have unequivocal evidence for sharp peaks with DMSO, while injection of any other solution (max 10µL) caused peak braoadening?