We have observed circular and linear magnetic dichroisms in angle-resolved photoemission spectra of 50-monolayer Gd films grown on Y(0001) and 6-monolayer Fe-Ni alloy films grown on Cu(001). The 4/level of Gd and the Fe 3
level of the Fe-Ni alloy were measured. A different geometry was used for the magnetic circular dichroism than was used to measure the magnetic linear dichroism. The geometries were chosen so that the magnetic circular dichroism is predicted to be closely related to the magnetic linear dichroism for four-fold symmetric Fe-Ni/Cu(001) but not for three-fold symmetric Gd-Y(0001). Experimental results are presented.