Nanolaminate composites with layer thicknesses down to 65 nm display conventional 3 stage creep behavior with creep resistance increasing as layer thickness decreases. A model for the time dependent high temperature deformation response of Cu-Nb composites is developed, and compared to creep tests performed on multilayers fabricated via accumulative roll bonding (ARB). The model assumes a continuous laminate structure of 50% Cu and 50% Nb in which deformation is controlled by stage II creep for the copper (ε˙cr=Aσn) and plasticity in Nb. Regimes in which composite steady-state creep at constant stress can be achieved are identified. The modeling illustrates that strain-hardening in the niobium plays a critical role in the transient response of the multilayer, which can dominate the creep lifetime. The combination of experiments and models strongly suggest that dislocation climb mechanisms in the copper control the time-response at 400 ∘C for all layer thicknesses tested.