We use the bond-fluctuation model to measure self-diffusivity of asymmetric blends of cyclic and linear polymers, where the number of monomers in the cyclic and linear polymer are different. We consider two series of asymmetric blends and vary the relative composition. In particular, N-C = 300 and N-L = 150, and N-C = 150 and N-L = 300, where N-C and N-L, are the number of monomers in the cyclic and linear polymers, respectively. Compared to cyclic polymers, the self-diffusivity of linear polymers is relatively insensitive to the blend composition, and is approximately within a factor of two of the pure linear self-diffusivity. In sharp contrast, the self-diffusivity of cyclic polymers exhibits a strong "order of magnitude" variation with the blend microenvironment. The latter data appear to be consistent with trends expected from previous simulations of symmetric cyclic-linear blends, as a function of the fraction of linear polymer. (C) 2013 Elsevier Ltd. All rights reserved.