Summary: In this paper, a stochastic scenario of relaxation underlying the generalization [R. Kahlau et al., “Generalization of the Cole-Davidson and Kohlrausch functions to describe the primary response of glass-forming systems”, J. Phys. Cond. Matters 22, No. 36, Article ID 365101 (2010; doi:10.1088/0953-8984/22/36/365101)] of the Cole-Davidson (CD) and Kohlrausch-Williams-Watts (KWW) functions is proposed. As it has been shown [loc. cit.], the new three-parameter time-domain fitting function provides a very flexible description of the dielectric spectroscopy data for viscous glass-forming liquids. In relation to that result we discuss a hierarchically-constrained model yielding the proposed relaxation fitting function. Within the “exponentially decaying relaxation contributions” framework we show origins of the high-frequency (short-time, respectively) fractional power law, i.e., the characteristic feature of the new, as well as, of both CD and KWW response functions. We also bring into light a reason for which their common behavior in the opposite frequency limit is linear on external field frequency. Finally, we relate the new relaxation pattern [loc. cit.] with the Generalized Gamma (GG) survival probability of an imposed, non-equilibrium initial state in a relaxing system.