The study investigates the onset of convection in a Maxwell nanofluid layer confined between two parallel plates. This investigation takes into account thermophoretic and Brownian diffusion and assumes no nanoparticle flux at the boundaries. The analysis involves two main approaches. Linear stability analysis, under which the Galerkin-type weighted residual technique, is employed to discuss the occurrence of both stationary and oscillatory convection for various parameters. Weakly nonlinear stability analysis, under which the truncated Fourier series is utilized. Heat and mass transfer are examined for both steady and unsteady states, with a focus on assessing Nusselt numbers for heat transfer and concentration Nusselt numbers for mass transfer. The results of the analysis are visualized through various graphical representations, including the streamline distribution, isotherm distribution, and isonano concentration distribution.