We discuss the use of thin film heterostructures for the generation of artificial multiferroic or magnetoelectric material systems. In this regard the transition metal oxides BiFeO₃ and BiCrO₃ are of particular interest. By using laser molecular beam epitaxy we have grown epitaxial thin films of these materials on SrTiO₃ substrates in a two-dimensional layer-by-layer growth mode. The films show small surface roughness and excellent crystallographic quality with mosaic spread below 0.04°. In contrast to the bulk materials, both BiFeO₃ and BiCrO₃ films have tetragonal crystal structure due to epitaxial coherency strain. The magnetic properties have been studied by SQUID magnetometry. In contrast to a previous report on BiFeO₃ we find only a small saturation magnetization below 0.05μ _B/formula unit both for BiFeO₃ and BiCrO₃, which can be explained by a canting of the antiferromagnetically aligned Fe and Cr spins, respectively. Furthermore, no indication for a strain induced enhancement of magnetization was found.