The cross-plane thermal conductivity of four Si/Si0.7Ge0.3 superlattices and three Si0.84Ge0.16/Si0.76Ge0.24 superlattices, with periods ranging from 45 to 300 and from 100 to 200 Å, respectively, were measured over a temperature range of 50 to 320 K. For the Si/Si0.7Ge0.3 superlattices, the thermal conductivity was found to decrease with a decrease in period thickness and, at a period thickness of 45 Å, it approached the alloy limit. For the Si0.84Ge0.16/Si0.76Ge0.24 samples, no dependence on period thickness was found and all the data collapsed to the alloy value, indicating the dominance of alloy scattering. This difference in thermal conductivity behavior between the two superlattices was attributed to interfacial acoustic impedance mismatch, which is much larger for Si/Si0.7Ge0.3 than for Si0.84Ge0.16/Si0.76Ge0.24. The thermal conductivity increased slightly up to about 200 K, but was relatively independent of temperature from 200 to 320 K.