The magnetic dynamics of La2CuO4 have been studied by means of inelastic neutron scattering in the energy range 0Latin small letter h with stroke140 meV. Experiments were carried out using a wide range of incident neutron energies so as to optimize the experimental resolution in each energy range studied. For energy transfers, Latin small letter h with stroke10 meV, and temperatures T in the range 5T320 K, we find that conventional spin-wave theory gives a good description of the magnetic dynamics. We obtain a low-temperature spin-wave velocity Latin small letter h with strokec=85030 meV. For low energies, Latin small letter h with stroke10 meV, and temperatures corresponding to the paramagnetic phase, our data indicate a response function consisting of overdamped spin waves and a quasielastic peak. © 1990 The American Physical Society.