The paper develops a theory of double-diffusive nanofluid convection in porous media. This theory is applied to investigating the onset of nanofluid convection in a horizontal layer of a porous medium saturated by a nanofluid for the case when the base fluid of the nanofluid is itself a binary fluid such as salty water. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, while the Darcy model is used for the porous medium. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. Both non-oscillatory and oscillatory cases are investigated by using Galerkin method; the stability boundaries for these cases are approximated by simple and useful analytical expressions.