The phase relationships involving the metastable orthorhombic (R-I) phase and the stable triclinic (T) phase were established for even-numbered carbon atom n-alkanes in the range of 8-20 carbon atoms. It is shown that the R-I phase behaves monotropically whatever the pressure and temperature (i.e., the R-I phase exhibits no stable pressure-temperature (P-T) region). Then, the incidence of the overall monotropic behavior of the RI phase on the construction of the temperature-composition (T-x) phase diagrams involving at least one even member was examined through four temperature-molar fraction (T-x) phase diagrams. Discussion on the location of the R-I-T-vapor (v) triple points in the P-T diagrams of this series of n-alkanes was determined and extended to higher even members.