The variational method of calculation of sensitivity coefficients connecting first variation of quality functional (the Bolts’s problem) with variable and constant parameters for multivariate non-linear dynamic systems described by interconnected difference ordinary equations and equations with distributed memory on phase coordi-nates and variable parameters is developed. Sensitivity coefficients are components of sensitivity functional and they are before variations of variable and constant parameters. The base of calculation of sensitivity coefficients is the de-cision of object equations in the forward direction of discrete time and corresponding difference conjugate equations for Lagrange’s multipliers in the opposite direction of discrete time.