A co-rotating scroll compressor, comprising: a driving-side scroll member configured to be driven by a drive unit so as to rotate, and comprising a plurality of spiral driving-side walls provided about a center of a driving-side end plate at predetermined angular intervals; a driven-side scroll member comprising spiral driven-side walls , the driven-side walls being provided about a center of a driven-side end plate at predetermined angular intervals and in a number corresponding to the driving-side walls , the driven-side walls being engaged with the corresponding driving-side walls so as to form a compression space; a synchronous driving mechanism configured to transmit driving force from the driving-side scroll member to the driven-side scroll member so that the driving-side scroll member and the driven-side scroll member rotationally move in a same direction at a same angular velocity; and a driving-side supporting member arranged across the driven-side end plate , fixed to free end sides of the driving-side walls in an arrangement direction, and rotated together with the driving-side scroll member , and/or a driven-side supporting member arranged across the driving-side end plate , fixed to a distal end side of the driven-side walls , and rotated together with the driven-side scroll member , wherein a fixing portion of each of the driving-side walls to which the driving-side supporting member is fixed is provided in a position close to a radially outside end portion of the driving-side wall and separated from the radially outside end portion in an inner circumferential direction of the driving-side wall , and/or a fixing portion of each of the driven-side walls to which the driven-side supporting member is fixed is provided in a position close to a radially outside end portion of the driven-side wall and separated from the radially outside end portion in an inner circumferential direction of the driven-side wall . a driving-side scroll member configured to be driven by a drive unit so as to rotate, and comprising a plurality of spiral driving-side walls provided about a center of a driving-side end plate at predetermined angular intervals; a driven-side scroll member comprising spiral driven-side walls , the driven-side walls being provided about a center of a driven-side end plate at predetermined angular intervals and in a number corresponding to the driving-side walls , the driven-side walls being engaged with the corresponding driving-side walls so as to form a compression space; a synchronous driving mechanism configured to transmit driving force from the driving-side scroll member to the driven-side scroll member so that the driving-side scroll member and the driven-side scroll member rotationally move in a same direction at a same angular velocity; and a driving-side supporting member arranged across the driven-side end plate , fixed to free end sides of the driving-side walls in an arrangement direction, and rotated together with the driving-side scroll member , and/or a driven-side supporting member arranged across the driving-side end plate , fixed to a distal end side of the driven-side walls , and rotated together with the driven-side scroll member , wherein a fixing portion of each of the driving-side walls to which the driving-side supporting member is fixed is provided in a position close to a radially outside end portion of the driving-side wall and separated from the radially outside end portion in an inner circumferential direction of the driving-side wall , and/or a fixing portion of each of the driven-side walls to which the driven-side supporting member is fixed is provided in a position close to a radially outside end portion of the driven-side wall and separated from the radially outside end portion in an inner circumferential direction of the driven-side wall . <EOS>