  Two manifestations of decoherence, called instantaneous and dynamical, are
investigated. The former reflects the suppression of the interference between
the components of the current state while the latter reflects that within the
initial state. These types of decoherence are computed in the case of the
Brownian motion and the harmonic and anharmonic oscillators within the
semiclassical approximation. A remarkable phenomenon, namely the opposite
orientation of the time arrow of the dynamical variables compared to that of
the quantum fluctuations generates a double exponential time dependence of the
dynamical decoherence in the presence of a harmonic force. For the weakly
anharmonic oscillator the dynamical decoherence is found to depend in a
singular way on the amount of the anharmonicity.
