Magnetic properties of polycrystalline samples of RuSr₂(Gd_1.5Ce_0.5)Cu₂O_10−δ, as-prepared (by solid-state reaction) and annealed (12 h at 845 °C) in pure oxygen at different pressure (30, 62 and 78 atm) are presented. The specific heat and magnetization were investigated in the temperature range 1.8–300 K with a magnetic field up to 8 T. The specific heat, C(T), shows a jump at the superconducting transition (with an onset at T≈37.5 K). Below 20 K, a Schottky-type anomaly becomes apparent in C(T). This low-temperature anomaly can be attributed to splitting of the ground term ⁸S_7/2 of paramagnetic Gd³⁺ ions by internal and external magnetic fields. It is found that curves C(T) taken for different values of magnetic field have the same crossing point (at T_*≈2.7 K) for all the samples studied. At the same time, C(H) curves taken for different temperatures have a crossing point at a characteristic field H_*≈3.7 T. These effects can be considered as a manifestation of the crossing point phenomenon which is supposed to be inherent for strongly correlated electron systems.