The magnetic structures of a series of Ho/Er alloys have been determined by neutron-diffraction techniques. The alloys were prepared as thin films (10000 Angstrom thick) by molecular beam epitaxy, and are single crystals with a mosaic spread of about 0.2 degrees. A variety of magnetic structures are found, arising from the competition between the exchange and anisotropic crystal-field interactions, the latter of which are of opposite sign for Ho and Er. The magnetic phase diagram has five distinct phases with long-range magnetic order: basal-plane helical, tilted helical, cycloidal, c-axis longitudinally modulated, and conical. The cycloid and tilted helix have both incommensurate and commensurate q = 1/4c* forms, and all of the thin films have a conical structure at low temperatures, even though corresponding films of pure Ho and Er do not exhibit this phase. There is a pentacritical point, and probably a disordered phase which is completely surrounded in the phase diagram by magnetic phases with long-range order. A Landau theory is developed to describe these results.