The effective mass and pole strength for protons and neutrons are evaluated in neutron matter for different densities. The source for the N-N interaction is the nonstatic one-boson-exchange model, and the many-body problem is treated self-consistently by looking simultaneously at the renormalization of the nucleons and the bosons in the medium. The π and ρ meson exchanges in the exchange channel are shown to play an important role in the energy and momentum dependence of the nucleon self-energy. The renormalization of the meson properties in the medium, especially the pion properties, stresses the energy dependence of the interaction, making retardation effects important at high densities. Some astrophysical implications of our results are also discussed.