The paper addresses a very important criterion for the evaluation of the tractive and economical performances of agricultural tractors, namely the potential performance characteristics, which represents the drawbar power curve depending on the drawbar pull. At a large scale, this curve coincides with the tractive efficiency of the tractor taking account of the drawbar pull. We herein present the mathematical modelling of the potential performance characteristics which is particularized for three types of tractors: two-wheel-drive tractor, four-wheel-drive tractor and caterpillar tractors. The mathematical modeling has a high degree of generalization: the final mathematical functions comprise only dimensionless parameters. Related graphs are subsequently presented and the three types of tractors are comparatively analyzed taking into account the tractive and economical performances. Considering the potential performance characteristics, we put forward proposals for an accurate design of a tractor transmission when establishing the number and structure of gears.