use warnings;
use strict;
use Data::Dumper;

my @lines = <DATA>;

my $n;
my %all_hash;
for (@lines) {
        chomp;
        if (/^>/) {
                $n = $_;
        } else {
                push @{ $all_hash{ $n } }, $_;
        }
}       
print Dumper(\%all_hash);

__DATA__
>seq1
ASDFGHASDFGHJ
ERTYUIOOIUYLK
NBGFEWERTY
>seq2
BGTNHYMJUKOPK
MNBFSDFGHJ