The authors consider the parallel acquisition of direct-sequence spread-spectrum signals with very low signal-to-noise ratio (SNR) and with frequency and pseudonoise chip clock epoch uncertainty due to Doppler. This problem arises in the context of low-earth-orbiting satellite-based mobile radio networks where the Doppler effect induces both large initial uncertainty and considerable dynamics during the acquisition. Because the Doppler affects both the carrier frequency and the chip clock epoch, the authors search over a 2-D uncertainty region, quantized in both dimensions so that the estimated process evolves in time over a lattice. Their approach exploits the fact that the Doppler dynamics of the signal can be modeled as a Markov process. Results leading to the probability of acquisition as a function of the acquisition time are obtained.