The authors develop a variant of Newton’s method in order to obtain traveling wave solutions of the differential-difference systems of the form \[ \dot u(\eta, t)- \gamma\Delta u(\eta, t)= L(u(\eta, t), u(\eta+ r_1, t),\dots, u(\eta+ r_N, t))- f(u(\eta, t),a), \] where \(L\) represents a linear difference operator. A typical example of the nonlinear operator \(f\) is \(f(u,a)= u(u- a)(u-1)\) with \(a\in (0,1)\). Numerical experiments illustrate the efficiency of the method. The references contain 43 items.