Supersonic random motions are observed in dark clouds and are traditionally interpreted as Alfve n waves, but the possibility that these motions are has not been ruled out. In this work we super-Alfve nic report the results of numerical experiments in two opposite regimes : and whereMach numberÈthe ratio of the rms velocity to the speed. Our results show Alfve nicAlfve n that models with are consistent with the observed properties of molecular clouds that we have M A ? 1 tested (statistics of extinction measurements, distribution of integrated antenna temperature, Zeemansplitting measurements of magnetic Ðeld strength, line width versus integrated antenna temperature of molecular emission-line spectra, statistical B-n relation, and scatter in that relation), while models with have properties that are in conÑict with the observations. We Ðnd that both the density and the M A D 1 magnetic Ðeld in molecular clouds may be very intermittent. The statistical distributions of the magnetic Ðeld and gas density are related by a power law, with an index that decreases with time in experiments with decaying turbulence. After about one dynamical time it stabilizes at B P n0.4. Magnetically dominated cores form early in the evolution, while later on the intermittency in the density Ðeld wins out, and also cores with a weak Ðeld can be generated by mass accretion along magnetic Ðeld lines.