The crystal structure of the low-temperature form of AgCuPO4 (i.e., -AgCuPO4) was determined by powder X-ray diffraction and was compared with that of the high-temperature form of AgCuPO4 (i.e., -AgCuPO4). The magnetic properties of the two forms were examined by measuring their magnetic susceptibilities and evaluating the relative strengths of their spin-exchange interactions on the basis of spin-dimer analysis. Both forms of AgCuPO4 have layers of Cu2P2O8 alternating with silver-atom double layers; -AgCuPO4 has two Cu2P2O8 layers per unit cell, while -AgCuPO4 has one. The coordinate environment of each Cu2+ ion is close to being a distorted square pyramid in -AgCuPO4, but it is close to being a distorted trigonal bipyramid in -AgCuPO4. The magnetic susceptibilities of - and -AgCuPO4 are well simulated by an antiferromagnetic alternating-chain model, which leads to J/kB = -146.1 K and J/kB = -75.8 K for -AgCuPO4, and J/kB = -82.6 K and J/kB = -31.7 K for -AgCuPO4 (with the convention in which the spin-exchange parameter between two adjacent spin sites is written as 2J). The spin gaps, /kB, obtained from these parameters are 93.7 K for -AgCuPO4 and 62.3 K for -AgCuPO4. The strongest spin exchange in both forms of AgCuPO4 comes from a super-superexchange path, and this interaction is stronger for -AgCuPO4 than for -AgCuPO4 by a factor of ~2, in good agreement with the experiment. Our analysis supports the use of this model for -AgCuPO4 and indicates that the spin lattice of -AgCuPO4 would be better described by a two-dimensional net made up of weakly interacting alternating chains.Read less <