#!/usr/bin/perl
use warnings;
use strict;
use feature qw(say);

my @strings = qw(xxxxxx.2012-50.yyyyy
                 xxxxxx.2012-51.yyyyy
                 xxxxxx.2012-52.yyyyy
                 xxxxxx.2013-1.yyyyy
                 xxxxxx.2013-2.yyyyy
                 xxxxxx.2013-3.yyyyy
                 xxxxxx.2013-4.yyyyy
                 xxxxxx.2013-10.yyyyy
                 xxxxxx.2013-11.yyyyy
                );

my @sorted = sort {
    my ($ay, $an) = $a =~ /\.([0-9]+)-([0-9]+)\./;
    my ($by, $bn) = $b =~ /\.([0-9]+)-([0-9]+)\./;
    $ay <=> $by or $an <=> $bn
} @string;

say for @sorted;
[download]

As this might be rather slow for larger lists, various technics exist to speed it up. One of them is called Orcish Maneuvre:

#!/usr/bin/perl
use warnings;
use strict;
use feature qw(say);

my @strings = qw(xxxxxx.2012-50.yyyyy
                 xxxxxx.2012-51.yyyyy
                 xxxxxx.2012-52.yyyyy
                 xxxxxx.2013-1.yyyyy
                 xxxxxx.2013-2.yyyyy
                 xxxxxx.2013-3.yyyyy
                 xxxxxx.2013-4.yyyyy
                 xxxxxx.2013-10.yyyyy
                 xxxxxx.2013-11.yyyyy
                );

my %cache;
my @sorted = sort {
    ($cache{$a} //= generate_key($a))
        cmp
    ($cache{$b} //= generate_key($b))
} @strings;

say for @sorted;

sub generate_key {
    my $s = (split /\./, shift)[1];
    my ($year, $number) = split /-/, $s;
    return $year . sprintf '-%03d', $number;
}
[download]

Update: Simple solution added.

As a small variant, you can calculate a key by 100*year+month, assuming that month will always be two digit at most...

my @sorted = sort {
    ($a =~ /\.([0-9]+)-([0-9]+)\./, 100*$1+$2) 
<=> ($b =~ /\.([0-9]+)-([0-9]+)\./, 100*$1+$2)
} @strings;
[download]

or would it be ok to insert the missing zero?

map { s/-(\d)\./-0\1./ } @strings;
my @sorted = sort @strings;
[download]

(Make sure the regexp does not match elsewhere in your strings.)

I assumed 3 digits in the second solution. 50 seems too big for a months to me (maybe a week?)
لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

Using the GRT:

print for @a;;
xxxxxx.2013-2.yyyyy
xxxxxx.2013-11.yyyyy
xxxxxx.2013-10.yyyyy
xxxxxx.2012-52.yyyyy
xxxxxx.2013-3.yyyyy
xxxxxx.2012-51.yyyyy
xxxxxx.2012-50.yyyyy
xxxxxx.2013-1.yyyyy
xxxxxx.2013-4.yyyyy

@b = map{ 
    unpack 'x[NN]a*', $_ 
} sort map{ 
    m[(\d{4})-(\d+)]; 
    pack 'NNa*', $1, $2, $_ 
} @a;;

print for @b;;
xxxxxx.2012-50.yyyyy
xxxxxx.2012-51.yyyyy
xxxxxx.2012-52.yyyyy
xxxxxx.2013-1.yyyyy
xxxxxx.2013-2.yyyyy
xxxxxx.2013-3.yyyyy
xxxxxx.2013-4.yyyyy
xxxxxx.2013-10.yyyyy
xxxxxx.2013-11.yyyyy
[download]

G'day luca76,

Your test data already appears to be sorted. Here's my take on a solution (with unsorted input):

$ perl -Mstrict -Mwarnings -E '
my @input = qw{
    xxxxxx.2013-2.yyyyy
    xxxxxx.2012-51.yyyyy
    xxxxxx.2013-10.yyyyy
    xxxxxx.2012-50.yyyyy
    xxxxxx.2013-1.yyyyy
};
say $_->[0] for sort { $a->[1] <=> $b->[1] or $a->[2] <=> $b->[2] }
    map { [ $_, split /-/, (split /\./)[1] ] } @input;
'
xxxxxx.2012-50.yyyyy
xxxxxx.2012-51.yyyyy
xxxxxx.2013-1.yyyyy
xxxxxx.2013-2.yyyyy
xxxxxx.2013-10.yyyyy
[download]

As perldoc -f sort will tell you, the sort verb in Perl takes a subroutine name or an in-line code block as its argument.   That piece of code is handed two variables named $a and $b corresponding to the two items now being compared, and it must return a value that is less than, equal to, or greater than zero.   Perl provides a special operator, <=>, specifically to assist with this.   Also cmp ... which compares strings.   (Do not get tripped-up by this peculiarity of Perl!)

The || operator is also useful because it is a “short-circuit logical-OR.”   If the expression on the left side is nonzero (“true”), the right side won't be evaluated.   Perfect for chaining comparisons together to sort by more than one field.

For anything but very simple cases, I prefer to define a separate sort-comparison subroutine, because an in-line code block can easily devolve into “chicken scratches.”   The code, however you choose to write it, should be extremely obvious, able to be tested in isolation, and also very easily changed.   It will be executed tens of thousands of times.

As perldoc -f sort will tell you, weak description of it, and stories about how I'm cool like that in the obviousness of my code I say I write but never post on perlmonks