#!/usr/bin/perl
use strict;
use warnings;
use IO::Handle;
use IO::Select;

my ($fname1, $fname2) = qw(1.txt 2.txt);
open my $fh1, $fname1 or die $!;
open my $fh2, $fname2 or die $!;

my $slct = IO::Select->new();
$slct->add($fh1, $fh2);

while (1) {
    my @canBeRead = $slct->can_read(); 
    foreach my $fh (@canBeRead) { 
        my $line = $fh->getline();
        if (defined $line) {
            my $fname = $fh == $fh1 ? $fname1 : $fname2;
            print "$fname: $line\n"
        } else {
            sleep 1;  # be nice
        }
    }
}