We discuss asymptotic solutions of nonlinear steady-state equations of the fluctuation dynamo, i.e. equations describing generation of a random magnetic field in a random mirror symmetric flow of conducting fluid. The flow is assumed to be locally homogeneous and isotropic and the correlation scalelis considered to be small in comparison to the size of the region occupied by the flow,L.These presumptions admit a closed nonlinear equation for the mean energy density of the magnetic field whose solutions are considered here forl/L≪ 1.