B.Baumgartner Postulates for Time-Evolution in Quantum Mechanics (41K, LaTeX) ABSTRACT. A detailed list of postulates is formulated in an algebraic setting. These postulates are sufficient to entail the standard time evolution governed by the Schr\"odinger- or Dirac equation. They are also necessary in a strong sense: Dropping any one of the postulates allows for other types of time-evolution, as is demonstrated with examples. Some philosophical remarks shall hint on possible further investigations.