The A 1S1 potential energy curve of AgH is studied by means of the second-order multistate multireference perturbation theory including the spin–orbit and relativistic effects. The anomalous behavior of the vibrational energy levels observed in experiment is reproduced well by theory. An analysis of the A 1S1 wave function shows that at the internuclear distance of 4–6 Å, a partial electron transfer from the 5pz orbital of silver to the 1s orbital of hydrogen occurs. This admixture of the ionic-like @core# 4d101sH 2 configuration occurring in A 1S1 due to two avoided crossings, namely X 1S1 with A 1S1 and A 1S1 with C 1S1, is found to be responsible for the unusual shape of the A 1S1 potential energy curve: the effective potential is a superposition of a Morse-like covalent interaction between Ag and H, and the electrostatic ionic-like interaction between Ag1 and H2. We present spectroscopic parameters, vibrational levels, and rotational constants computed for a large number of vibrational levels and observe good agreement with available experimental data. The equilibrium distance agrees within 0.01 Å and the vibrational frequency within 60 cm21 for the state-specific calculations. Larger relative discrepancy is observed for vexe , about 30 cm21 , however the non-Morse-like nature of the energy curve makes it impossible to describe the levels only with v and vexe , so that direct comparison is not well defined.