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We have investigated the effects of Co substitution for Ga on the structural and the superconducting properties of (Ga1.yCoy)Sr2(Tm1.xCax)Cu2Oz (x = 0.25, 0.3; 0  y  0.6) prepared under ambient pressure. Partial substitution of Co for Ga is found not only to improve the phase purity of the sample but also to induce superconductivity in GaSr2(Tm1.xCax)Cu2Oz. On progressive replacement of Ga by Co at a fixed Ca content, the room-temperature thermoelectric power decreases at first and then increases at higher Co-doping content, indicating that the carrier concentration on the superconducting planes is sensitive to the substitution of Co for Ga. The superconducting behavior of the Co-substituted samples is discussed in connection with the structural properties and the oxygen contents of the samples.