Low-frequency features of the phonon spectra of disordered solid solutions and heterogeneous crystalline structures are analyzed at the microscopic level. It is shown that boson-peak type excitations can arise in disordered solid solutions whose sites have only translational degrees of freedom. Thus it is established that such excitations appear mainly because of the additional positional dispersion of sound waves which is due to the disordering. The influence of boson-peak excitations on the low-temperature specific heat is investigated. It is found that in a number of cases the specific heat is more sensitive to excitations of this kind than the low-frequency density of states is. It is shown that anomalies similar to Ioffe-Regel' crossover and boson peaks can also arise in disordered heterogeneous crystalline structures with a complicated lattice.