Single crystals of the binary and pseudobinary compoimds RAlg and RxRx'1-xAl2, where R and R' are rare-earth metals, have been grown by the Czochralski technique. Measurements of the magnetostrictions and anisotropies of disc-shaped samples of the compounds GdAl2, Gd0.98 Tbg0.02 and Gdg0.95Tbg0.95 Al2 have been made between 4.2K and their Curie temperatures in applied magnetic fields up to 2.5T. Anisotropy constants were measured by means of a torque magnetometer. The methods by which anisotropy constants can be derived from torque curves were investigated using a well-documented single crystal of cobalt and the conclusions drawn were applied to the measurements on the rare-earth alloys. The derived values of the first two anisotropy constants of GdAl2 were K1 = (-2.8 +- 0.1) x 103 J m-3 and K2 = (-1-4 +- 0.2) x lO-3 J m-3 at 0 K. Magnetostriction measurements were performed using resistive strain gauges and a precision D. C. Wheat stone bridge circuit. The values of the first two magnetostriction constants of GdAl2 are h1 = (6.0 +- 0.2) x 10-6 h2 = (-25.1 +- 0.2) x 10-6 at 4.2K. The dilute alloys were measured in the same way and derived values of their anisotropies and magnetostrictions were used to determine the anisotropy constant and the first two magnetostriction constants of TbAl2. The values are K1 = - 2 x 107 +- 10% J m-3 ; h1 = I4OO x 10-6 ; h2 = 920 x 10-6. The method used to derive these values and a theoretical model developed to test its validity is also discussed