How to run 2 compute shaders in one frame

Hello,
what’s the best way to have two compute shaders running within one frame, where the second compute shader depends on date from the first one…?

I tried that but the resulting texture is always a frame or so behind the engines rendering…
I have two rendering devices… I run the first compute shader to calculate data to feed into the second compute shader…

so basicaly like this:

compute shader 1:
update data buffer with x
dispatch
sync
read data from Buffer… xyz for compute shader 2

compute shader 2:
update data Buffer with xyz
dispatch
sync
read data from buffer… for texture
write to texture
display texture
=> texture out of sync with sytem rendering