The acceleration of particles to high energy by relativistic plasma waves has received a great deal of attention lately. Most of the particle-acceleration schemes using relativistic plasma waves rely either on intense terawatt or petawatt lasers or on electron beams as the driver of the acceleration wave. These laboratory experiments have attained accelerating fields as high as 1 GeV cm−1 with the electrons being accelerated to about 100 MeV in millimetre distances. In space and astrophysical plasmas, relativistic plasma waves can also be important for acceleration. A process that is common to both laboratory and space plasmas is the surfatron concept, which operates as a wave acceleration mechanism in a magnetized plasma. In this paper, we present test-particle results for the surfatron process.