Electromagnetic waves in layered superconductors are known as Josephson plasma waves (JPWs). An important property of JPWs is the gap in their energy spectrum: JPWs can propagate if the frequency is above the Josephson plasma frequency J (refs 1, 2), which being in the terahertz (THz) range, is important for applications3. This feature is fuelling a growing interest in studies of JPWs (see, for example, refs 4–7). However, nonlinear (NL) JPWs have not yet been studied. It is a challenge to understand nonlinearities around the plasma frequency, where the interplay between the unusual spectrum and the nonlinearity of the JPWs is most pronounced. Here, we predict the propagation of NL JPWs with frequencies below J, which is unusual for plasma-like excitations. In analogy to NL optics, these waves exhibit numerous remarkable features, including the slowing down of light (when the group velocity /k0), self-focusing effects and the pumping of weaker waves by stronger ones. The nonlinearity for >J can potentially be used for transforming continuous THz radiation into amplified pulses.