Abstract <p>The paper considers anomalous scale effects for fibrous and dispersed nanomaterials with a gradient interphase layer caused by the dispersion and aggregation of inclusions. To model these effects and evaluate the mechanical properties of dispersed and fibrous composites with interphase layer, an analytical-numerical algorithm has been developed that allows one to obtain an exact solution to the cell problem in the Bakhvalov asymptotic homogenization method. This algorithm is used to evaluate and simulate the effective characteristics of structurally inhomogeneous materials taking into account the aggregation of the filling nanoparticles, when non-classical effects of strengthening occur at ultra-small volume fractions. The obtained solutions also allow one to calculate the stress concentration tensor that reproduces the distribution features of local stresses near inclusions taking into account the gradient properties of the interphase layer. It is of great importance for evaluating the strength characteristics of such materials. Using the developed algorithm a study was conducted of the anomalous properties of polymethyl methacrylate filled with multilayer carbon nanotubes, and for the first time, the presence of two enhancement waves of the mechanical properties for the composite with ultra-low filler fractions was noted, which is confirmed by the similar behavior of metal-matrix composites based on an aluminum matrix and oxide fillers.</p>