A new three-parameter family of cosmological models is found, which are solutions of Einstein-Maxwell equations in a space-time filled with electrically neutral stiff matter. They generalize an anisotropic homogeneous cosmology without electromagnetic field by Vajk and Eltgroth [J. Math. Phys. 11, 2212 (1970)] and support a conjecture about proportionality of electromagnetic four-potential of an Einstein-Maxwell solution and the Killing vector of a corresponding space-time with stiff matter. This conjecture turns out to be the clue to a new solution-generating method of Einstein-Maxwell fields with sources. © 1990 American Institute of Physics.