The variational method of calculation of sensitivity coefficients connecting first variation of quality functional with variations of variable and constant parameters for multivariate non-linear dynamic systems described by generalized difference equations with the distributed memory on phase coordinates and variable parameters is developed. The nonlinear quality functional also has a generalized form. Sensitivity coefficients are components of sensitivity functional and they are before variations of variable and constant parameters. The base of sensitivity coefficients calculation are the decision of generalized equations of the object model in the forward direction of discrete time and corresponding difference conjugate equations for Lagrange’s multipliers in the opposite direction of discrete time.