Zero-field–cooled magnetization, magnetic relaxation, and ac susceptibility measurements have been performed on a Mn 12-Ac oriented powdered sample as a function of temperature, field, and orientation. Magnetization jumps and susceptibility peaks have been observed about magnetic-field values B n= nB 1, where B 1≈ 5 kG. These anomalies are due to the existence of relaxation rate maxima near B n. From these experimental results we infer the existence of resonant spin tunnelling between degenerate excited levels of opposite spin orientation.