A stacked semiconductor module is made by stacking a second semiconductor device having a second semiconductor chip mounted to the top surface of a second semiconductor substrate above the top surface of a first semiconductor device having a first semiconductor chip mounted to a first semiconductor substrate. The top surface of the first semiconductor substrate is provided with a first connection terminal and the bottom surface of the first semiconductor substrate is provided with an external connection terminal. A region of the bottom surface of the second semiconductor substrate lying opposite to the second semiconductor chip is provided with a second connection terminal. A conductive connecting member connects the first connection terminal to the second connection terminal.