Thanks Everyone. Borrowing from what you have suggested, really helped. I now know where I was screwing up at. How can I delete something when I have skipped it first? That was a good question and a wrong way to think. so thank for your help. If you want to see what the rewritten code looks like, here you go.

#!/usr/bin/perl -w

$dir = "(directory path)";

print "Starting Delete Process\n\n";

opendir(DIR, "$dir") || die "No $dir: $!";
@files = grep(!/^\./, readdir(DIR));
@files = sort @files;
closedir(DIR);

foreach (@files)
{
    print $_, "\n";
        if (/\.log$/i || /\.\d+\w+\-\d+\wm$/i || /\.txt$/i)
        {
        unlink ("$dir/$_") if (-f "$dir/$_") || 
            print "Unable to delete $_: $!";
    }
}
[download]

Basicly, this script will now delete any log file, date-time file, or text file found in a predetermined directory. Thanks once again for your help.