Tb1-xDyxZn(01-xDyx alloys exist in the hexagonal phase, with the c-axis extremely hard, whereas for Tb1-xDyxFe2, a cubic Laves phase alloy, very hard <111> axes can be changed to very hard <100> axes by increasing x from 0 to 1. (In fact, the existence of a near zero magnetic anisotropy by the proper choice of x is the origin of the well-known Terfenol-D alloys, Tb1-xDyxFe2). The Tb$1-x)DyxZn system discussed here is particularly attractive because of the simplicity of its crystal structure (CsCl), its relatively high Curie temperatures (for rare earth alloys), and the existence of a large (uv0) phase for T < 50K. A summary of some of the important properties of these three alloy systems is given in Table I. In all these systems, at least one of the magnetostriction constraints is very large.