Under RedHat 5.1 and 5.2 in the procedure killproc() (used
during shutdown) the following code appears:

  # TERM first, then KILL if not dead
  kill -TERM $pid
  usleep 100000
  if ps h $pid >/dev/null 2>&1 ; then
          sleep 3
          kill -KILL $pid
  fi

i.e., send TERM, see if it's gone away 100ms later, and if
not *wait another three seconds* then send KILL (AIUI). This
has been giving me 'kill: (nnn) - No such pid' errors during
shutdown (not surprisingly).