A new model that describes nonlinear adsorption and pore and surface diffusion (including concentration-dependent diffusion) in a single particle was derived using an intraparticle quartic concentration profile approximation and a summation of the gas and adsorbed phases in the material balances. Analytical expressions were obtained for the fractional uptake and adsorbed-phase concentration profile, and a differential expression was obtained for the rate of accumulation in the adsorbed phase that can be used as an accurate simplification in fixed-bed adsorption models. The new model was tested against the exact numerical solution for a variety of adsorbate-adsorbent systems and a broad range of bulk concentrations, with the results always being far superior to those obtained with the LDF approximation and even those obtained with a similarly derived model based on a parabolic profile approximation. This was especially the case at short times, where the other models failed to capture the behavior of the exact solution. The success of this new model was attributed to a set of assumptions that allowed more of the physics to be retained, while still making the solution tractable. This approach led to very useful and also very accurate analytical and differential expressions for nonlinear adsorption and diffusion phenomena.