I am looking for a RegEx which search for 'ax', not followed by 'ba' and preplaces this string.

If I may, I'll reword this to what you actually want: "I am looking for a RegEx which searches for 'ax' followed by two chars which are not "ba". In that case, here's a solution:

use strict;
use warnings;

use Test::More;
$\="\n";

#  search for 'ax', not followed by 'ba'
my @teststr = ('0axba',      # simple not ok
               '1axbb',      # one char ok, one not 
               '2axccaxdd',  # simple 2 times
               '1axbaxcc',   # one time (sequence combined)
               '1axcaxcc'    # one time (sequence combined)
              );

my @reg = ( qr/ax(?!ba)/,     # look ahead
            qr/ax[^b][^a]/,   # 2 not char sets
            qr/ax(?!ba)../,   # look ahead plus 2 chars
         );

plan tests => @teststr*@reg;

for my $re (@reg)
{ print "---------------\n$re\n---------------";
  for my $str (@teststr)
  { my $str1=$str; my $str2=$str; # get teststring
    $str1=~s/^\d//;               # remove result
    my $got = $str1=~s/$re/-/g;   # replace (do test)
    $str2=~s/^(\d)//;             # remove result and remember
    cmp_ok($got, '==', $1, "($1) $str2 => $str1  ");  #check
} }
[download]

So you were really very close.