  We consider the equation of the Jeffreys type as the basic one in three
different models of mass transfer, namely, the Jeffreys type and two-phase
models, and the $D_1$ approximation to the linear Boltzmann equation. We study
two classic 1 + 1D problems in the framework of each model. The first problem
is the transfer of a substance initially confined in a point. The second
problem is the transfer of a substance from a stationary point source. We
calculate the mean-square displacement (MSD) for the solutions of the first
problem. The temporal behaviour of the MSD in the framework of the first and
third models is found to be the same as that in the Brownian motion described
by the standard Langevin equation. Besides, we find a remarkable phenomenon
when a portion of the substance does not move.
