The concept of an accelerator using a travelling magnetic wave that acts on magnetized projectiles is discussed. Although superconductors potentially may be good projectile material, their low critical temperature makes them unsuitable, Among ferromagnetic materials, dysprosium seems superior. For stable suspension and guidance, a high conductivity (preferrably superconducting) guide sheet is necessary. Magnetic field gradients of 109A/m2travelling at 106m/s should be achievable using present state-of-the-art components; resulting accelerations are ≳500 km/s2. A linear accelerator for final speeds of 50 km/s needs a length of 2.5 km. Guidance forces sufficient to produce acceleration of m/s2allow circular accelerators of reasonable size to achieve hypervelocities for small (50-100 mg) projectiles. An accelerator of 170-m diam would surpass the best results from light gas guns. Travelling waves suitable for accelerations of 104m/s2can be produced without switching by means of flux displacing rotors and may be easily adapted to circular accelerators.