The kinematics of two-body nucleon-nucleon scattering inside an excited nucleus are calculated. Closed-form expressions are deduced for energy and angular distributions of nucleons following single two-body scattering. The Pauli principle is taken into account in deducing these expressions. The kinematical effects of creation and annihilation of particle-hole pairs are shown explicitly. The results for single scattering are extended to multiple two-body interactions through appropriate recursive relations. The expressions derived can be used to calculate the energy spectra and angular distributions of nucleons emitted in nucleon-induced and heavy-ion fusion reactions.