We have performed electrical resistivity measurements at different pressures on two kinds of samples (low-T-c and high-T-c), which differ in physical properties of the heavy-fermion superconductor CeCu2Si2. It was found that one with lower T-c shows partial derivative T-c/partial derivative P of negative and the other with higher T-c shows partial derivative T-c/partial derivative P of positive. Therefore, the superconductivity for these two samples may have different origins. (C) 2003 Elsevier B.V. All rights reserved.