We discuss the relations between weighted mean methods and ordinary convergence for double sequences. In particular, we study
Tauberian theorems also for methods not being products of the related one-dimensional summability methods. For the special
case of theC1,1-method, the results contain a classical Tauberian theorem by Knopp  as special case and generalize theorems given by Móricz
 thereby showing that one of his Tauberian conditions can be weakened.