The quality of service (QoS) of Web services is a key factor of their success. This requires to design new methods in order to study it. Here we propose families of upper bounding models for the response time of composite Web services for two kinds of composition: the statical and random « fork and merge ». In the r st case, the complexity of bounding models belongs to O(n p n) where n is the number of called services whereas the complexity of the exact model belongs to O(n2). In the second case, the complexity of bounding models still belongs to O(n p n) whereas the complexity of the exact model belongs to O(n3). Furthermore, having a family of bounding models allows to choose the bounding model depending on the parameters of the exact model. The numerical results show the interest of our approach w.r.t. complexity and accuracy of the bound.