gistfile1.sh

#!/bin/bash

# You could use array indices with any version of bash:

declare -a processes
filenames=( dir/* )
for filenum in "${!filenames[@]}"; do
  filename=${filenames[filenum]}
  run_step1 "$filename" > "${filename}.out" &
  processes[filenum]=$!
done

for filenum in "${!filenames[@]}"; do
  filename=${filenames[filenum]}
  wait "${processes[filenum]}" && # Check the exit status
  run_step2 "${filename}.out" > "${filename}.result"
done

# Or you could use associative arrays with bash 4:
declare -A processes
for f in dir/*; do
  run_step1 "$f" > "${f}.out" &
  processes[$f]=$!
done

for f in "${!processes[@]}"; do # The ! gets us the keys
  wait "${processes[$f]}" && # Check the exit status
  run_step2 "${f}.out" > "${f}.result"
done