  Fundamental modifications of the standard Schr\"odinger equation by
additional nonlinear terms have been considered for various purposes over the
recent decades. It came as a surprise when, inverting Abner Shimony's
observation of "peaceful coexistence" between standard quantum mechanics and
relativity, N. Gisin proved in 1990 that any (deterministic) nonlinear
Schr\"odinger equation would allow for superluminal communication. This is by
now the most spectacular and best known anomaly. We discuss further anomalies,
simple but foundational, less spectacular but not less dramatic.
