You should use the context setting as in http://api.jquery.com/jQuery.ajax/
function doop(){
var old = $(this).siblings('.old').html();
var newValue = $(this).siblings('.new').val();
$.ajax({
url: 'doop.php',
type: 'POST',
context: this,
data: 'before=" + old + "&after=" + newValue,
success: function(resp) {
if(resp == 1) {
$(this).siblings(".old').html(newValue);
}
}
});
return false;
}
“this” will be transfer to the success scope and will act as expected.