We present a mobility resilient deterministic broadcast algorithm with worst-case time complexity of O ( n log n ) for ad hoc networks where the nodes possess collision detection capabilities; n is the total number of nodes in the network. The algorithm is based on a breadth-first traversal of the network and allows multiple simultaneous transmissions by the nodes. The idea of this broadcast algorithm is then extended to develop a mobility resilient deterministic gossiping algorithm having O ( D n log n ) worst-case run time ( D is the diameter of the network graph), which is an improvement over the existing algorithms. Simulation results show that on an average, the time for completing the broadcast or gossiping is significantly lower than the theoretical worst-case time requirement.