The alternating one-dimensional Heisenberg S = 1/2 chain compound with spin gap, (VO)(2)P2O7, has been studied by the high-field magnetization and P-31 NMR measurements. Two critical phenomena at 25 +/- 1 and 46 +/- 2 T are observed in the magnetization curve, which are considered to be a crossover between the ground state and the excited state in two kinds of gap systems. P-31 NMR also revealed the coexistence of two magnetic systems with independent spin gaps. Results obtained from the present and previous studies are well explained by the model in which two kinds of magnetic chains along the b axis behave as alternating spin chains with independent gap energies.