The effect of higher harmonics on the shape of Poincaré maps (first return maps) derived from current self-oscillations has been investigated in a semiconductor superlattice system driven by a dc + ac voltage bias. In addition to the intrinsic fundamental frequency, a number of higher harmonics with comparable amplitude are observed. The current oscillation traces are simulated according to the power spectra in order to determine the effect of the higher harmonics on the Poincaré maps. The calculated Poincaré maps for quasiperiodic oscillations as well as frequency locking are clearly distorted by the presence of the higher harmonics. The shape of the distorted Poincaré maps agrees with the experimentally observed ones. The calculation also reveals that the phase shift between the different frequency components of the current has an important effect on the shape of the Poincaré maps. © 1998 The American Physical Society.