By using the coincidence degree theory of Mawhin and some analytical skills,this paper studies the existence of periodic solutions to a class of nonlinear second order differential equations with delays as follows,x''(t)+f(t,xt)[x'(t)]n+a(t)x3(t)+b(t)x2(t)+c(t)x(t)=p(t)(n>2),some sufficient theorems for the existence of at least three periodic solutions to this equation are given.