The method of molecular dynamics is used to investigate the stability and physical properties of (CH4)i(H2O)n clusters. The possibility of methane molecules being absorbed by clusters containing ten and twenty water molecules is demonstrated. Such clusters retain the thermodynamic stability when the number of CH4 molecules they absorbed does not exceed six. The frequency dispersion of complex permittivity of (CH4)i(H2O)n aggregates reflects the resonant behavior of polarizability depending on the applied electric field. The dependence of the absorption coefficient α on the frequency of infrared radiation varies significantly after even one CH4 molecule is absorbed by water clusters. The maximal value of α for water aggregates which absorbed CH4 molecules is much lower than the respective value for pure water clusters of appropriate size.