In this paper the iterates of the q-Durrmeyer operators are introduced using a modification. For these iterates the convergence results are obtained. The estimates for the rate of convergence are obtained in terms of the modulus of smoothness. A Voronovskaya type asymptotic result is obtained. Finally necessary conditions are derived which guarantee the convergence of these iterates to the projection operators. © 2016, The National Academy of Sciences, India.