Summary: Multistate life table models, which follow persons through more than one living state, have found increasing use in demographic analyses. Multistate stable populations, however, are infrequently used because the constant rate assumption is quite strong and such populations can take centuries to approach stability. Dynamic models, that is models where the rates can change over time, are examined to derive a new solution for the size and composition of a multistate population in terms of the sequence of underlying population projection matrices (PPMs). Constraints on the subordinate eigenvalues and the subordinate eigenvectors of the time-varying PPMs produce a model population that grows according to the dominant eigenvalues of each time-specific PPM and has a state composition that depends only on the most recent PPM. The two living state model is examined in detail, relationships between the PPM elements and the size and composition of the model are explored, and two illustrative applications of the model are presented.