Experimental vapour-liquid, solid-fluid, and solid-liquid-vapour equilibrium data of the binary system (methane + tetracosane) in the temperature range 315-450K and for pressures up to 200MPa are presented. The experiments were carried out for various mixtures with compositions ranging from almost pure methane to pure tetracosane. It was found that the (solid alpha-to-solid beta) transition of pure tetracosane has hardly any influence on the shape of the (solid + fluid/fluid) boundary curves and the three-phase equilibrium curve (solid tetracosane + liquid + vapour) of the binary system. The second critical endpoint of the three-phase curve (s(C24) + 1 = g), where solid tetracosane is in equilibrium with a critical fluid phase was located at a temperature of T = (322.60 +/- 0.25) K, a pressure of p = (104.7 +/- 0.4) MPa, and a mole fraction of tetracosane in the critical fluid phase of x(C24) = (0.041 +/- 0.003).