The Cu spin magnetism in La2−x−yEuySrxCuO4 (x ≤ 0.17; y ≤ 0.2) has been studied by means of magnetization measurements in fields up to 14 Tesla. Our results clearly show that in the antiferromagnetic phase Dzyaloshinsky-Moriya (DM) superexchange causes Cu spin canting not only in the LTO phase but also in the structural low-temperature phases LTLO and LTT. In La1.8Eu0.2CuO4 the canted DM-moment is about 50% larger than in pure La2CuO4 which we attribute to the larger octahedral tilt angle in the Eu-doped compound. We also find clear evidence that the size of the canted DM-moment does not change significantly at the structural transition at TLT from LTO to LTLO and LTT. The most important change induced by the transition is a significant reduction of the magnetic coupling between the CuO2 planes. As a consequence, the spin-flip transition of the canted Cu spins which is observed in the LTO phase for magnetic field perpendicular to the CuO2 planes disappears in the LTT phase. The shape of the magnetization curves changes from the well known spin-flip type to a weak-ferromagnet type. However, no spontaneous weak ferromagnetism is observed even at very low temperatures, which seems to indicate that the interlayer decoupling in our samples is not perfect. Nonetheless, a small fraction ( 15%) of the DM-moments can be remanently magnetized throughout the entire antiferromagnetically ordered LTT/LTLO phase, i.e. for T < TLT and x < 0.02. It appears that the remanent DM-moment is perpendicular to the CuO2 planes. For magnetic field parallel to the CuO2 planes we find that the critical field of the spin-flop transition decreases in the LTLO phase, which might indicate a competition between different inplane anisotropies. To study the Cu spin magnetism in La2−x−yEuySrxCuO4, a careful analysis of the Van Vleck paramagnetism of the Eu 3+ ions was performed.