We extend to delay equations recent results obtained by G. Feltrin and F. Zanolin for second-order ordinary equations with a superlinear term. We prove the existence of positive periodic solutions for nonlinear delay equations -u″(t) = a(t)g(u(t), u(t - τ)). We assume superlinear growth for g and sign alternance for a. The approach is topological and based on Mawhin's coincidence degree. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.