The Licensed Assisted Access (LAA) is shown as a required technology to avoid overcrowding of the licensed bands by the increasing cellular traffic. Proposed by 3GPP, LAA uses a Listen Before Talk (LBT) and backoff mechanism similar to Wi-Fi. While many mathematical models have been proposed to study the problem of the coexistence of LAA and Wi-Fi systems, few have tackled the problem of QoS provisioning, and in particular analysed the behaviour of the various classes of priority available in Wi-Fi and LAA. This paper presents a new mathematical model to investigate the performance of different priority classes in coexisting Wi-Fi and LAA networks. Using Discrete Time Markov Chains, we model the saturation throughput of all eight priority classes used by Wi-Fi and LAA. The numerical results show that with the 3GPP proposed parameters, a fair coexistence between Wi-Fi and LAA cannot be achieved. Wi-Fi users in particular suffer a significant degradation of their performance caused by the collision with LAA transmissions which has a longer duration compared to Wi-Fi transmissions. © 2018 IEEE.