We study the linear stability of a fluid to double-diffusive convection in the case for which the background temperature field is linear, but the mean salt distribution is a nonlinear function. A variety of idealized limits amenable to perturbative treatment are examined, and a detailed numerical study of a hyperbolic tangent profile is presented. It is shown that nonlinearity in the background salinity profile leads to pronounced competition and interaction between the linear normal modes. ©1998 American Institute of Physics.