The self-consistent methods are used for the construction of nonlocal effective property operators of matrix composite materials with respect to the space and time variables. Spatial nonlocality is pronounced for the external fields which characteristic scale change has the order of the correlation radius of the random set of inhomogeneities. The effective field method is used for the construction of the operator of the effective elastic stiffness that is nonlocal with respect to space variables. The effective medium method is used for the solution of the non-stationary homogenization problem in the case of composites with spherical inclusions by action of time-varying external fields. The time nonlocality can be observed by the action of space-localized impulses on composite materials. The corresponding fields are substantially different from Green’s functions of the homogeneous medium with stationary parameters. The difference is notable at short time intervals from the moment of excitation, and it tends to diminish with time. The diminishing rate depends on the contrast in the thermo-conductivity properties of the matrix and inclusion materials. Examples of impulse excitations of matrix composites are considered.