Polymer-metal composites offer the possibility of strongly enhanced nonlinear optical properties, which can be used for ultrasmall photonic devices. In this paper, we investigate numerically, by means of the finite-difference time-domain (FDTD) method, the propagation characteristics of surface plasmon polariton (SPP) modes excited in an optical nanowire consisting of a chain of either metallic cylinders or metallic spheres embedded in dielectric shells made of polymers (or other material) with optical Kerr nonlinearity. Our FDTD calculations incorporate both the nonlinear optical response of the dielectrics as well as the frequency dispersion of the metals, which is considered to obey a Drude-like model. It is demonstrated that, in the linear limit, the nanowire supports two SPP modes, a transverse and a longitudinal one, separated by Δλ = 20 nm. Furthermore, the dependence of the transmission of these SPP modes, on both the pulse peak power and Kerr coefficient of the dielectric shell, is investigated. Nonlinear optical phenomena, such as power-dependent mode frequency, switching, or optical limiting, are observed.