The steady mixed convection boundary-layer flow on a vertical circular cylinder embedded in a porous medium filled by a nanofluid is studied for both cases of a heated and a cooled cylinder. The governing system of partial differential equations is reduced to ordinary differential equations by assuming that the surface temperature of the cylinder and the velocity of the external (inviscid) flow vary linearly with the axial distance x measured from the leading edge. Solutions of the resulting ordinary differential equations for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction phi, the mixed convection or buoyancy parameter lambda and the curvature parameter gamma. Results are presented for the specific case of copper nanoparticles. A critical value lambda (c) of lambda with lambda (c) < 0 is found, with the values of | lambda (c)| increasing as the curvature parameter gamma or nanoparticle volume fraction phi is increased. Dual solutions are seen for all values of lambda > lambda (c) for both aiding, lambda > 0 and opposing, lambda < 0, flows. Asymptotic solutions are also determined for both the free convection limit (lambda >> 1) and for large curvature parameter (gamma >> 1).