We investigate the impact of nonlinear thermal radiation and variable transport properties on the two-dimensional flow of an electrically conducting Casson nanofluid containing gyrotactic microorganisms along a moving wedge. In some previous studies, it has been assumed that the fluid viscosity and thermal conductivity are temperature dependent. However, this study assumes that the fluid viscosity, thermal conductivity, and the nanofluid properties, are dependent on the solute concentration. Some experimental studies have shown that the viscosity and thermal conductivity of nanofluids are strongly dependent on the volume fraction of nanoparticles rather than just the temperature. The spectral local linearization method is used to solve the conservation equations. We compare our results with those in the literature, and we discuss the convergence and accuracy of the spectral local linearization method. The impact of some parameters on the skin friction, heat and microorganisms mass transport is discussed.