If an incident wavefield hits a curved interface that possesses certain inflection points, there may exist 'nonspecular' events in the reflected field that cannot be explained by real ray theory. The magnitude of such events can reach the order of the specular ones and can be expressed in terms of specular reflections at certain points on the analytic continuation of the interface. In fact, specular reflected 'complex rays,' connecting complex reflection points with the observation point, are used to explain such events. Previous results obtained for acoustic calculations, involving an incident plane wave and a perfectly soft reflector, are extended to arbitrary velocity and density contrasts, as well as to an incident far-field cylindrical wavefield. Moreover, the agreement between analytic results and independent computations using a finite-differences scheme is shown. It confirms the existence of nonspecular reflections. The interpreter of a seismic section should, therefore, be aware of not attributing a subsurface interface to a nonspecular reflection, e.g., at a flank of a saltdome.