Potential electron scattering by P2 and P3 phosphorus molecules at scattering energies of 0.5-30 eV has been studied theoretically for the first time. The research is carried out in the framework of the independent-atom model and using a real parameter-free relativistic optical potential for the electron interaction with atoms in the molecule. For the consistent description of the electron scattering by the atoms in the molecule, the potential parameters and the atomic characteristics are calculated in the local approximation of the stationary and time-dependent variants of the density functional theory. The comparison of the angular behavior of the differential cross-sections and the energy dependences of the integral ones in the cases of electron scattering by phosphorus molecules and phosphorus atoms testifies to their similarity. K e y w o r d s: independent-atom model, optical potential, scattering amplitude, partial phase shift, differential and total cross-sections, optical theorem.