  This paper identifies and investigates nature of the transition between
Gaussian and exponential forms of decoherence. We show that the decoherence
factor (that controls the time dependence of the suppression of the
off-diagonal terms when the density matrix is expressed in the pointer basis
representation) can be described by the convolution of Gaussian and exponential
functions, their contributions modulated by the strength of the
system-environment interaction. In the strong and weak coupling limits,
decoherence reduces to the familiar Gaussian and exponential forms,
respectively. The mechanism is demonstrated with two paradigmatic examples of
decoherence -- a spin-bath model and the quantum Brownian motion.
