  In the paper explicit functional continuous Runge-Kutta and
Runge-Kutta-Nystr\"om methods for retarded functional differential equations
are considered. New methods for first order equations as well as for second
order equations of the special form are constructed with the reuse of the last
stage of the step. The order conditions for Runge-Kutta-Nystr\"om methods are
derived. Methods of orders three, four and five which require less computations
than the known methods are presented. Numerical solution of the test problems
confirm the convergence order of the new methods and their lower computational
cost is performed.
