The problem of existence of
-periodic solutions for the two delay differential equations
is investigated. The results which are proved by using a slight modification of an abstract result due to R. K. Nagle
and Z. Sinkala
[Differential Equations: Stability and Control, Proc. Int. Conf., Colorado Springs/CO (USA) 1989, Lect. Notes Pure Appl. Math. 127, 401-408 (1990; Zbl 0711.34053
)] extend some known results obtained for bounded perturbations of forced harmonic oscillators at resonance and for similar problems where the perturbations involve the derivative of the solution.