MPEJ Volume 10, No. 8, 20 pp. Received: Aug 15, 2002. Revised: Nov 5, 2003. Accepted: Nov 18, 2004. S. Klimek Quantum Dynamical Systems with Quasi-Discrete Spectrum ABSTRACT: We study totally ergodic quantum dynamical systems with quasi-discrete spectrum. We investigate the classification problem for such systems in terms of algebraic invariants. The results are noncommutative analogs of the theory of Abramov. http://www.maia.ub.es/mpej/Vol/10/8.ps http://www.maia.ub.es/mpej/Vol/10/8.pdf http://www.ma.utexas.edu/mpej/Vol/10/8.ps http://www.ma.utexas.edu/mpej/Vol/10/8.pdf http://mpej.unige.ch/mpej/Vol/10/8.ps http://mpej.unige.ch/mpej/Vol/10/8.pdf