The composition dependence of the optical and structural properties of Ge1-xSix nanocrystals is investigated by means of ab initio total-energy and electronic-structure calculations. A trimodal distribution of the Ge-Ge, Ge-Si, and Si-Si bond lengths is found. The pair-excitation energies and the Stokes shift are calculated taking into account many-body and alloying effects. They show a distinct nonlinear behavior with changing composition. The radiative lifetime decreases exponentially with increasing Ge molar fraction. The theoretical results explain recent photoluminescence measurements. They show that composition and confinement effects can be discussed nearly separately.