In this work we study the existence of new periodic solutions for
the well knwon class of Duffing differential equation of the form
x′′+cx′+a(t)x+b(t)x3=h(t), where c
is a real parameter, a(t), b(t) and h(t) are continuous
T--periodic functions. Our results are proved using three
different results on the averaging theory of first order.