This work presents a review of literature data of methane and carbon dioxide hydrate equilibrium at low temperatures. Constants of Arrhenius-type equation accurately determined for the mentioned lines which allow calculating the hydrate equilibrium pressure at any temperature below the quadruple point for both systems contain ice or supercooled water. Through intersection analysis, new accurate quadruple points were determined. Interpretations based on flash calculations by high accurate equations of states shown enthalpies of clathrate formation/dissociation, for equilibrium below quadruple point, lead to the similarity of Clapeyron and Clausius-Clapeyron approaches. Based on equality of equilibrium conditions at the quadruple point, new hydration numbers were calculated. Gamma-phi approach through high accurate equations of states of GERG-2008 and CG for the prediction of VHIw three-phase equilibrium line was evaluated. Commercial packages of Multiflash and PVTsim and open-source codes of CSMGem and CSMHYD were used to model the phenomena. [ABSTRACT FROM AUTHOR]