If your flow analyzer got two separate layer for Annexin V or PI, you have no need to do such compensation, e.g. analyze cells without PI or annexin V. 

However, most analyzer always use one layer for both annexin V and PI stimulation, to avoid the signal crossover, such compensation works are necessary.

thank you for your answers. 

However, I have one more questions. I am transfecting my cells with a miRNA mimic (or a negative control mimic).

Can I use untransfected cells as negative controls and single stain controls or should I use negative-control-mimic-transfected cells?

The pictures I send you were done a long time ago using a very old FACS calibur. I treated cells with doxorubicin that strongly induces apoptosis.

Now, we got a new instument with 6 laser (violet, blue, green and red). I have to check this, but I do not think that I will need any compensation.

I have never used both PI and AnnexinV- this is completely new for me.

I found out that I have to compensate. I hope that I find someone here at the institute who can show me how I have to do it.

@Filip: May I send you my data to be sure that I do the compensation properly?

you definitively have to include controls of  your two populations (transfected or not) using single staining. Often dead cells result in auto fluorescence and you have to take this into account when running this type of experiments. have you try substituting PI for 7AAD? In many cytometers 7AAD can be detected in FL3-FL4 and the croos-over from FL1 is lower in that case ,resulting in easier compensations