The problem of existence of

$2\pi $-periodic solutions for the two delay differential equations

${x}^{\text{'}\text{'}}\left(t\right)+x\left(t\right)+{h}_{1}\left(x(t-r)\right)+{h}_{2}\left(x(t-s)\right)=p\left(t\right)$ and

${x}^{\text{'}\text{'}}\left(t\right)+x\left(t\right)+h\left(x(t-r)\right)+g({x}^{\text{'}}(t-s)=p\left(t\right)$ 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.