• You aren't actually iterating over anything. Try 'while(<FILE1>)' rather than just 'while()'.
• The second filehandle won't reset on each iteration of the outer loop. Try slurping the data into an array / hash instead.
• You didn't use code tags. Try reading the FAQ.

#!/usr/bin/perl -w

use strict;

open(FILE1,"/tmp/file1") or die "Couldn't open /tmp/file1: $!";
open(FILE2,"/tmp/file2") or die "Couldn't open /tmp/file2: $!";

my @array;
my %hash;

while (<FILE1>) {
  chomp;
  push @array, $_;
}

while (<FILE2>) {
  chomp;
  $hash{$_} = '';
}

close FILE1;
close FILE2;

foreach (@array) {
  if(exists $hash{$_}) {
    print "$_ matched!\n"
  } 
}
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