We consider here numerical methods for systems of retarded functional differential equations of two equations in which the right-hand sides are cross-dependent of the unknown functions, i.e. the derivatives of unknowns don’t depend on the same unknowns. It is shown that using the special structure of the system one can construct functional continuous methods of Runge–Kutta type with fewer stages than it is necessary in case of general Runge–Kutta functional continuous methods. Order conditions and example methods of orders three and four are presented. Test problems are solved, demonstrating the declared convergence order of the new methods.