The phase transformations and the shape memory effect in In-rich Pb alloys and In rich-Sn alloys have been studied by means of X-ray diffractometry supplemented by metallographic observations. The alloys containing 12~15 at.%Pb transform from the ${alpha}_2$ (fct) phase to the ${alpha}_1$ (fct) phase by way of an intermediate phase (m phase) on cooling. The results of X-ray diffraction show that the metastable intermediate phase is observed both on cooling and heating, and has a face-centered orthorhombic (fco) structure. It is concluded that the ${alpha}_1{ ightleftarrows}{alpha}_2$ transformation is expressed by the ${alpha}_1{ ightleftarrows}m{ ightleftarrows}{alpha}_2$ transformation both on usual cooling and heating with the rate more than $8{ imes}10^{-3}$ K/s. The $m{ ightleftarrows}{alpha}_2$ transformation takes place with a mechanism involving macroscopic shear and are of diffusionless (martensitic) type. The temperature hysteresis in the two transformations is 10~13 K between the heating and cooling transformations. The alloys containing 0~11 at.%Sn are -phase solid solutions with a face centered tetragonal structure (c/a > 1) at room temperature, the axial ratio increasing continuously with tin content. The In-(11~15) at.%Sn alloys are mixtures of ${alpha}$ and ${eta}$ phases, the ${eta}$ phase having a f. c. tetragonal structure (c/a < 1). The alloys containing more than 15 at.%Sn are ${eta}$-phase solid solutions. The In-(12.9~15.0) at.%Sn alloys show a shape memory effect only when quenched to the temperature of liquid nitrogen, although their effect becomes weak and finally disappears after keeping at room temperature for a long time. The ${eta}{ ightarrow}{alpha}^{prime}$ phase transformation is of the diffusionless (martensitic) type, and takes place between 330 K at 12.9 at.%Sn and 150 K at 14.5 at.%Sn. The hysteresis of transformation temperatures on heating and cooling is considerably large (29~40 K), depending on the composition. Both In-Pb and In-Sn alloys showed distinct the shape memory effects.