We have found solutions to the problem of a relativistic pulsar wind interacting with a nebula moving at constant velocity vn. The wind is assumed to contain a toroidal magnetic field; the ratio of Poynting flux to particle flux in the wind is a constant σ. Under these assumptions, the wind is shocked at a radius rs that moves out at constant velocity. Solutions for the shocked wind are only possible if σ < σc = 1/(−1 + c/vn). For a given value of vn, rs → as σ → σc. Kennel and Coroniti (1984) have calculated similar models for the Crab Nebula but they assume that rs is a constant; i.e. they calculate steady-state models. The steady-state approximation is expected to be good close to the shock wave, but it breaks down in the outer parts of the nebula. For vn = 2000 km s−1 and rn/rg = 20, Kennel and Coroniti find σ = 0.003. For the same Crab Nebula pmeters, our time-dependent model yields σ = 0.0016. There may be times in the evolution of Crab Nebula or of other pulsar nebulae when a model with a shocked relativistic wind and a toroidal magnetic field cannot apply. It appears that a wide variety of structures are possible for pulsar nebulae.