By means of a simple model calculation we estimate the amplitudes of nonlinear de Haas--van Alphen oscillations in heavy-fermion compounds, i.e., oscillations that correspond to linear combinations of ordinary closed orbits of the Fermi surface. Two possible many-body mechanisms are discussed: (i) frequency mixing via the nonlinear field dependence of the magnetization (Shoenberg effect), and (ii) the modulation of the antiferromagnetic order parameter. The incipient antiferromagnetic order in many heavy-fermion compounds at low T provides a nonlinear coupling mechanism that may lead to cross-sectional areas corresponding to differences of ordinary extremal closed orbits of the Fermi surface.