Protein synthesis-dependent, late long-term potentiation (LTP) and depression (LTD) at glutamatergic hippocampal synapses are well characterized examples of long-term synaptic plasticity. Persistent increased activity of protein kinase M xcexb6 (PKMxcexb6) is thought essential for maintaining LTP. Additional spatial and temporal features that govern LTP and LTD induction are embodied in the synaptic tagging and capture (STC) and cross capture hypotheses. Only synapses that have been tagged by a stimulus sufficient for LTP and learning can capture PKMxcexb6. A model was developed to simulate the dynamics of key molecules required for LTP and LTD. The model concisely represents relationships between tagging, capture, LTD, and LTP maintenance. The model successfully simulated LTP maintained by persistent synaptic PKMxcexb6, STC, LTD, and cross capture, and makes testable predictions concerning the dynamics of PKMxcexb6. The maintenance of LTP, and consequently of at least some forms of long-term memory, is predicted to require continual positive feedback in which PKMxcexb6 enhances its own synthesis only at potentiated synapses. This feedback underlies bistability in the activity of PKMxcexb6. Second, cross capture requires the induction of LTD to induce dendritic PKMxcexb6 synthesis, although this may require tagging of a nearby synapse for LTP. The model also simulates the effects of PKMxcexb6 inhibition, and makes additional predictions for the dynamics of CaM kinases. Experiments testing the above predictions would significantly advance the understanding of memory maintenance.