AbstractAfter a review of first order short periodic errors, the mathematical model for higher order short periodic errors caused by multipath signals is developed. The effects of multipath signals are explained by two theoretical examples. Practical results of short periodic error determinations are given. First and higher order long periodic errors have also been detected, with amplitudes up to 5 mm for cyclic errors with wavelengths of 1 km. Long periodic errors seem to account for a significant part of non-periodic errors previously attributed to phase inhomogeneities.