The extremely high data rates of optical computing technology (100 Mwords/s and upward) present unprecedented challenges in the dynamic memory design. An optical fiber loop used as a delay line is the best candidate for primary, dynamic memory at this time. However, it poses special problems in the design of algorithms due to synchronization requirements between the loop data and the processor. We develop a theoretical model, which we call the loop memory model (LLM), to capture the relevant characteristics of a loop-based memory. An important class of algorithms, ascend/descend—which includes algorithms for merging, sorting, discrete Fourier transformation (DFT), matrix transposition, and multiplication and data permutation—can be implemented without any time loss due to memory synchronization. We develop both sequential and parallel implementations of ascend/descend algorithms and some matrix computations. Some lower bounds are also demonstrated.