Something like this:

# assuming you've got the files open in handles $fh1 and $fh2
while (1) {
    last unless defined($line_from_file_1 = <$fh1>);
    last unless defined($line_from_file_2 = <$fh2>);
    # ...
}
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Basically you just use the "read a record" operator (<>, aka diamond operator) on each file handle. See also readline.