Similar to the idea given by bart and dwm042 above but a slightly different implementation using a hash of hashes with multiple values per key.

#!/usr/bin/perl -w

use strict;

my @list_of_files =  qw(file1.txt file2.txt);
my %data;
my $file_num = 0;

foreach my $file_name(@list_of_files){
    $file_num++;
    my $file = 'File'.$file_num;
    my $iter;
    my $flag = 0;

    open FH, $file_name or die "Cannot open $file_name. $!";
    while(<FH>){
        chomp;
        if($_ =~ /(Iteration.+)/){
            $iter = $1;
            $flag = 1;
            next;
        }
        if(/^$/){ $flag = 0; }
        if($flag){ push( @{$data{$iter}{$file}}, $_ ); }
    }
    close FH;
}

foreach my $iter ( sort keys %data ) {
    print "$iter\n";
    my $size;
    my $index = 0;
    do {
         for my $file ( sort keys %{ $data{$iter} } ) {
            print "$file: ", @{$data{$iter}{$file}}[$index], " ";
            $size = $#{$data{$iter}{$file}};
        }
        $index++;
        print "\n";
    }
    while($index<=$size);
    print "\n";
}
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