We studied magnetism of two cuprates using inelastic neutron scattering and magnetization measurements on powder samples. A spin gap of 6.2 meV (72 K) was observed in β-AgCuPO4. The spin system was determined as a spin-1/2 twofold-period (alternating) antiferromagnetic (AF) chain with two exchange interaction values of 80 and 14 K. Contrary to common knowledge, the strongest exchange interaction exists in a Cu–Cu bond with the distance of 5.20 Å in spite of the existence of short Cu–Cu bonds. Cu3(P2O6OD)2 is known to have a spin-1/2 threefold-period chain with J1-J2-J2 interactions, where J1 and J2 denote two AF exchange interaction parameters, showing a 1/3 magnetization plateau. A spin gap of 9.8 meV (114 K) was found, which generated the magnetization plateau. The gap corresponds to a singlet-triplet-like excitation of an AF dimer formed by the dominant J1 interaction. We determined that J1=111 K and J2=30 K. [ABSTRACT FROM AUTHOR]