This talk considers the numerical treatment of the differential equation that describes the motion of electric particles in a strong magnetic field. A standard integrator is the Boris algorithm which, for small stepsizes, can be analysed by classical techniques. For a strong magnetic field the solution is highly oscillatory and the numerical integration is more challenging. New modifications of the Boris algorithm are discussed, and their accuracy and long-time behaviour are studied with means of modulated Fourier expansions. Emphasis is put on the situation where the stepsize is proportional to (or larger than) the wavelength of the oscillations.