An anomaly in the heat capacity of Eu1.2Mo6S8 at ∼120 K (T0) has been observed and identified as a structural transformation. The heat capacity, electrical resistance, and Hall coefficient for the Eu-rich pseudoternaries have been measured under pressure to obtain the pressure dependence of T0. The depression of T0 by pressure is used to explain the pressure dependence of the superconducting transition temperature and the anomalous temperature dependence of the critical field.