Works fine for me with a 32 bit build of Perl 5.10.1 on 64 bit Windows 7:

use strict;
use warnings;
use 5.010;

open my $outFile, '>', 'delme1.txt';
print $outFile join ("\n", map "File 1 line $_", 1 .. 3), "\n";
close $outFile;
open $outFile, '>', 'delme2.txt';
print $outFile join ("\n", map "File 2 line $_", 1 .. 3), "\n";
close $outFile;

local @ARGV = ('delme1.txt', 'delme2.txt');

while (<>) {
    print $_;
}
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Prints:

File 1 line 1
File 1 line 2
File 1 line 3
File 2 line 1
File 2 line 2
File 2 line 3
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