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Abstract This paper studies the existence of positive periodic solutions of the following delayed differential equation: u′+a(t)u=f(t,u(t−τ(t))), $$ u'+a(t)u=f\bigl(t,u\bigl(t-\tau (t)\bigr)\bigr), $$ where a,τ∈C(R,R) $a, \tau \in C(\mathbb{R},\mathbb{R})$ are ω-periodic functions with ∫0ωa(t)dt=0 $\int_{0}^{\omega }a(t)\,dt=0$, f:R×[0,∞)→R $f:\mathbb{R}\times [0, \infty)\to \mathbb{R}$ is continuous and ω-periodic with respect to t. By means of the fixed point theorem in cones, several new existence theorems are established. Our main results enrich and complement those available in the literature.