We report results for ab initio molecular-dynamics simulations of SiGe liquid alloy (l-SiGe) near its melting point, and the amorphous alloy (a-SiGe) near absolute zero. The structural and electronic properties of l-SiGe and a-SiGe, diffusion constants for Si and Ge atoms in the liquid state, and dielectric functions for a-SiGe are presented and compared to previous calculations and to experiment. We find l-SiGe has a predominantly random structure with a slight phase separation of Si-Si and Ge-Ge bonds. Also, it is shown that the conductivity of l-SiGe has a metallic character and a-SiGe has a semiconductor-type conductivity. We predict diffusion constants for Si and Ge in l-SiGe near the melting point to be D$_{Si}$ = 1.9 × 10$^{-4}$ cm$^2$/s and D$_{Ge}$ = 1.5 × 10$^{-4}$ cm$^2$/s. Upon cooling, the structure of l-SiGe changes significantly from a more close packedlike structure to an open tetrahedral arrangement of atoms with more Si-Si and Ge-Ge association than in the melt. Our total pair correlation function for a-SiGe agrees well with available experiment.