From magnetization (M) and magnetostriction (lambda) measurements as a function of magnetic field and stress, the temperatures of anisotropy compensation, T(m), for technologically important Tb(x)Dy1-x(Fe(1-y)T(y)1.9 [T = Co, Mn (0.3 less-than-or-equal-to x less-than-or-equal-to 0.5) (0 less-than-or-equal-to y less-than-or-equal-to 0.3)] were determined. Measurements of M and lambda encompassing T(m) were made under compressive stresses from 8.8 to 36 MPa and for temperatures from - 196 to + 130-degrees-C. In agreement with earlier measurements, T(m) decreases with increasing Tb. Substitution of Mn for Fe for fixed x also decreases T(m). In contrast with these observations is the increase of the anisotropy compensation temperature with the replacement of Fe by small amounts of Co. In the cases of both (1) increasing Tb content and (2) increasing Co content, the Curie temperature T(C) increases, yielding, in general, a higher magnetic moment and saturation magnetostriction of these alloys. Thus, compensation at a given temperature may be obtained in an improved class of Laves phase compounds, R(x)(1)R1-x(2)(Fe(1-y)Co(y))2, where rare earths R(1) and R(2) are, for example, Tb and Dy.