2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134778Group classification of systems of two coupled nonlinear reaction-diffusion equation with a general diffusion matrix started in papers math-ph/0411027,, math-ph/0411028 is completed in present paper where all non-equivalent equations with triangular diffusion matrix are classified. In addition, symmetries of diffusion systems with nilpotent diffusion matrix and additional first order derivative terms are described.24 pages, 10 tablesMathematical Physics35K05; 35K55; 35Q55Group classification of systems of non-linear reaction-diffusion equations with general diffusion matrix. III. Triangular diffusion matrixtext