We have calculated the slowing-down densities of neutrons in two adjacent media of different slowing-down properties according to the age theory. The outer medium is extended to infinity. The inner medium consists of a sphere of radius a, and contains a monoenergetic fast neutron-source in the form of a concentric spherical shell of radius R.The method of Laplace transformation is used in solving the problem. The results are given by the expansions (25), (25′), (28) & (28′), which converge rapidly for those cases we usually meet with.For a concrete case where the two media are heavy water and graphite, and the fast neutron-source is of energy 2 Mev, numerical results for the slowing-down densities at thermal energy are obtained and compared with those obtained by the usual two-group approximation (Fig. 1, 2 & 3).