Another approach (using a regex, and assuming you want to keep the whitespace):

#! perl
use strict;
use warnings;

my $string = <<END;
> abcd1234
abcd abcd 
>xyz123 
xyz
END

if ($string =~ />(.*?)\n(.*?)>/s)
{
    print "First  substring is '$1'\n";
    print "Second substring is '$2'\n";
}
[download]

Output:

 0:23 >perl 497_SoPW.pl
First  substring is ' abcd1234'
Second substring is 'abcd abcd
'

 0:23 >
[download]

Hope that helps,