You can use regular expression capturing, and backreferences.

if( 
    $string =~ m/
                  \b([[:alpha:]]+)\b  # Match and capture word
                  .*?                 # Skip what you don't need
                  \b\1\b              # Match the captured word
                /x
  ) {
    print $1, "\n";
}
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Limitation: Words can contain only alpha characters. You could modify the expression: [[:alpha:]] so as to include what you might consider to be legal word characters, such as ' (apostrophe) and - (hyphen). I used the /x modifier to facilitate grouping the regular expression's sub-expressions into meaningful clusters so that it's easier to read.

Hope this helps!

use Scalar::Util qw( looks_like_number );

my %h;
$h{$_}++ for split /\t/, $string;

print "$_\n" for
    grep { $h{$_}>1 and !looks_like_number($_) }
    sort keys %h;
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In this particular example, since the words are tab-separated, I'd probably use a brute-force approach and split the string, then step through the resulting array, incrementing a hash. Admittedly, this is not a very efficient solution for any significant amount of data.

use strict;
use warnings;
my $string = 'LOCAL    Antony    17    Antony    23    1569';
my @tokens = split /\t/,$string;
my %duphash = ();
foreach (@tokens) {
  $duphash{$_}++;
}
[download]

Now %duphash has a 1 for each unique value and something greater than 1 for any duplicates.

Update: I ignored your requirement for skipping over numbers -- adjust accordingly.

Admittedly, this is not a very efficient solution for any significant amount of data.

For large — increasingly large — amounts of data, it's better than the regex with backref solution (e.g. as presented by davido). Put simply, the split-hash approach is O(n), whereas the regex-backref approach is O(n²)

We're building the house of the future together.

Sorry guys, my mistake.
What I want is only to know if the string has something more than one times.
I understand that you split the string using tab as delimiter, but what must I do to check if the array that is produced and contains all elements of the string has any duplicates in it? Just that, I don't want to know what the dulicates are, I only want to know if there are any...