A systematic approach intented to determine the mechanism by which ternary additions increase the strength of Ni3Al is presented. Uniaxial tensile and compressive flow stress measurements at constant strain rate were performed on single crystals of Ni3Al containing additions of Hf, Ta, Zr, and B, and also on binary Ni-rich Ni3Al. Data were collected over temperatures ranging from liquid nitrogen to 1100C, for different orientations within the standard unit triangle, different amounts of ternary additions as well as a function of the sense of the applied uniaxial stress. In agreement with previous studies, the yield strength of binary Ni3Al presented a positive temperature dependence up to about 800C. The critical resolved shear stress (CRSS) for the 111110 slip was found to be orientation dependent, mostly over the positive temperature range (200C up to 800C). Additions of ternary elements are found to enhance the CRSS of octahedral slip with much less effect on the CRSS for cube slip. The temperature of the maximum CRSS as well as the orientation of the stress axis for which the tension-compression asymmetry is zero are both found to be composition dependent. The value of the octahedral CRSS measured at low temperatures exhibits a strong dependence on both composition and orientation of the stress axis. The tension-compression asymmetry, taken as a measurement of the rate of cross slip, is affected by the ternary additions, specially Ta and Hf, and mostly at intermediate temperatures. At low temperatures the asymmetry is almost zero in most cases. For orientations in which the tension-compression asymmetry was found to be zero, the increase of the octahedral CRSS with ternary additions is believed to be a consequence of a lattice parameter/modulus mismatch mechanism.