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This paper presents the results of specific-heat and magnetization measurements, in particular their field-orientation dependence, on the first discovered heavy-fermion superconductor CeCu2Si2 (T-c similar to 0.6K). We discuss the superconducting gap structure and the origin of the anomalous pair-breaking phenomena, leading, e.g., to the suppression of the upper critical field H-c2, found in the high-field region. The data show that the anomalous pair breaking becomes prominent below about 0.15 K in any field direction, but occurs closer to H-c2 for H parallel to c. The presence of this anomaly is confirmed by the fact that the specific-heat and magnetization data satisfy standard thermodynamic relations. Concerning the gap structure, field-angle dependencies of the low-temperature specific heat within the ab and ac planes do not show any evidence for gap nodes. From microscopic calculations in the framework of a two-band full-gap model, the power-law-like temperature dependencies of C and 1/T-1, reminiscent of nodal superconductivity, have been reproduced reasonably. These facts further support multiband full-gap superconductivity in CeCu2Si2.
