An optimization problem with nonlinear utility is investigated in the well-known Ramsey vintage capital model described by nonlinear Volterra integral equations with an unknown function in the lower integration limits. The necessary and sufficient condition for an extremum is proven and a qualitative analysis is provided. A balanced growth case is found and a turnpike theorem is established for this problem. The obtained results demonstrate new phenomena as compared with the case of the linear utility optimization. © 2008 Taylor & Francis.