Probably you are trying to do the wrong thing. You should almost never need to reread a file in a nested loop like that. Most likely what you need to do is read file2 into a hash then use hash lookups to check for matches in file1. Something like:

use strict;
use warnings;

my $data1 = <<DATA;
1 a
2 b
3 c
DATA
my $data2 = <<DATA;
4 d
1 x
DATA

my %data2Hash;

open my $infile2, '<', \$data2;
while (<$infile2>) {
    chomp;
    my ($key, $tail) = split ' ', $_, 2;
    $data2Hash{$key} = $tail;
}
close $infile2;

open my $infile1, '<', \$data1;

while (<$infile1>) {
    chomp;
    my ($key, $tail) = split ' ', $_, 2;

    if (exists $data2Hash{$key}) {
        print "Matched $key: $data2Hash{$key}, $tail\n";
    }
}
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Prints:

Matched 1: x, a
[download]