We propose several variations of the adversarial queueing model. The priority model takes into account the case in which the packets can have different priorities, assigned by the adversary at injection time. The variable priority model is an extension of the priority model in which the adversary may change the priority of packets at each time step. The failure and reliable models are designed to cope with dynamic networks in which the adversary controls, under different constraints, the edge failures. We address stability issues in the proposed adversarial models. We show that the set of universally stable networks in the adversarial model remains the same in the priority, variable priority, failure and reliable models. From the point of view of queueing policies we show that several queueing policies that are universally stable in the adversarial model remain so in the priority, failure and reliable models. However, we show that LIS, a universally stable queueing policy in the adversarial model, is not universally stable in any of the other models. Moreover, we show that no greedy queueing policy is universally stable in the variable priority model. Finally we analyze the problem of deciding stability of a given network under a fixed protocol. We provide a characterization of the networks that are stable under FIFO and LIS in the failure model (and therefore in the reliable and priority models). This characterization allows us to show that the stability problem under FIFO and LIS in the failure model can be solved in polynomial time.