The parameters of many-body potentials for fcc and hcp transition metals, based on the second-moment approximation of a tight-binding Hamiltonian, have been systematically evaluated. The potential scheme, cast in analytical form, allows us to reproduce correctly the thermal behavior of transition metals making use of a small set of adjustable parameters. The large cutoff, which extends the range of the interactions up to the fifth-neighbor distance, ensures good quantitative agreement with the experimental data up to temperatures close to the melting point. The ability of the potentials to describe real systems has been checked by calculating point-defect properties, lattice dynamics, and finite-temperature behavior, and by comparing the results with other potential schemes. Application of this scheme to bcc transition metals has proved unsuccessful. Examples of derivation of many-body potentials for a few transition-metal alloys with cubic structure are also reported.