Abstract: We consider the problem of task assignment in heterogeneous multiple unmanned aerial vehicle (multi-UAV) systems, in which the tasks form disjoint groups. We establish a MUAP-GT (multi-UAV task assignment problem for grouped tasks) model. The objective is to maximize the total payoff where the number of tasks by a UAV is constant. We present a distributed auction algorithm for the MUAT-GT model based on dual decomposition, where the UAV system has a shared memory. The shared memory is removed, and a totally distributed algorithm is generated. Simulation results indicate the effectiveness and convergence of the proposed method.