In this paper, we prove the existence of two positive T-periodic solutions of an electrostatic actuator modeled by the time-delayed Duffing equation ẍ(t)+fD(x(t),ẋ(t))+x(t)=1−eV2(t,x(t),xd(t),ẋ(t),ẋd(t))x2(t),x(t)∈]0,∞[where xd(t)=x(t−d) and ẋd(t)=ẋ(t−d), denote position and velocity feedback respectively, and V(t,x(t),xd(t),ẋ(t),ẋd(t))=V(t)+g1(x(t)−xd(t))+g2(ẋ(t)−ẋd(t)),is the feedback voltage with positive input voltage V(t)∈C(R/TZ) for e∈R+,g1,g2∈R, d∈0,T. The damping force fD(x,ẋ) can be linear, i.e., fD(x,ẋ)=cẋ, c∈R+ or squeeze film type, i.e., fD(x,ẋ)=γẋ/x3, γ∈R+. The fundamental tool to prove our result is a local continuation method of periodic solutions from the non-delayed case (d=0). Our approach provides new insights into the delay phenomenon on microelectromechanical systems and can be used to study the dynamics of a large class of delayed Liénard equations that govern the motion of several actuators, including the comb-drive finger actuator and the torsional actuator. Some numerical examples are provided to illustrate our results.