I want to redirect output of my script to two logfiles.
I tried this :
./run.sh -c APP | tee >(grep " " > AppLogs.log) >(grep "XYZ" > xyz.log) >dev/null
but this does not solve my purpose because logfile xyz.log remains empty untill i stop my script, i want both files, AppLogs.log and xyz.log, to grow together.
someone plz help me doing this.

echo "this is log" | tee -a file1 file2

i am using grep to filter data, in this case file1 and file2 will contain same data..

You could try something like this:

./run.sh -c APP | 
  awk '/ / { print > "AppLogs.log" }
       /XYZ/ { print > "xyz.log"  }
       '

Previous awk is good and if your need both "grep" can be true in same line, then previous do it. Awk is excellent when you have group of rule and need to make every rule or only some / input record.

This shell example do only one of cases. (case is "multi grep")

> xyz.log
> AppLogs.log

./run.sh -c APP | while read line
do
        case "$line" in
                *XYZ*) echo "$line" >>  xyz.log ;;
                *" "*)   echo "$line" >> AppLogs.log ;;
        esac
done