We present specific heat and low field magnetic measurements on amorphous DyCu, DyAu, and DyNi alloy films. The magnetic contribution to the specific heat shows clearly that there are strong crystal fields effects in these systems. The highly anisotropic Dy alloys are compared to Gd alloys with similar exchange interactions but much weaker random anisotropy effects. Magnetic measurements on these two types of amorphous systems in the same field and temperature range show that they have characteristically different behavior. Using Arrot plots of our low field data we find that the Gd alloys all show evidence of spontaneous magnetization below TC. The highly anisotropic Dy alloys do not develop a spontaneous moment at any temperature, a result in agreement with the theory of Aharony and Pytte.