grep invading my ps

When I'm checking for some process, I usually write

ps aux | grep myprocess

And sometimes I get the output of

eimantas 11998  0.0  0.0   8816   740 pts/0    S+   07:45   0:00 grep myprocess

if the process is not running.

Now I really wonder why grep is in the list of processes if it filters out the output of the ps command after ps has run?