Solution accuracy is an important issue in modeling complicated, nonlinear physical phenomena such as double-diffusive processes. Recent researches in the area of internal, natural convection heat and mass transfer suggest that spectral methods may be a sound alternative to classical numerical schemes such as finite differences and finite element or, sometimes, the single one currently available. The present work is aimed at assessing the ability of the spectral approach to solving strongly coupled double-diffusive convection processes previously analyzed by finite element methods. The good agreement with data reported in literature for the cases we investigated shows that Chebyshev collocation (pseudospectral) representation that was used results in a very accurate and reliable numerical scheme, with much potential in addressing transient regimes and nonlinear effects. When efficiently implemented, it leads to very performant, vectorized computer codes.