Second-order solutions for internal and surface waves in a two-fluid system are derived using a perturbation technique. As expected, solutions of the second order are composed of the products of the first-order components. Super- and subharmonic transfer functions describing the relation between the first- and second-order wave amplitudes are introduced. For the self interaction of the first-order waves with a fixed wavenumber, there exist three combinations of linear waves. The associated superharmonic transfer function and the effects of second-order waves on wave profiles are examined. Furthermore, taking the density of the upper layer to be zero, present results include most existing theories for second-order surface waves as special cases.