A process produces an amide or lactam by subjecting an oxime compound to rearrangement in a solvent in the presence of: at least one catalyst selected from the group consisting of an aromatic compound (A1) containing a leaving group bound to a carbon atom constituting the aromatic ring, the aromatic ring including, as a constitutive atom thereof, a heteroatom or including, as a constitutive atom thereof, a carbon atom bound to an electron-withdrawing group, and a compound (A2) containing a structure of Formula (1): -G-LA (1) wherein G represents P, N, S, B or Si atom; and LA represents a leaving group, wherein G is bound to one or more atoms or groups in addition to LA; and a co-catalyst including a halogen-containing organic acid, to give the corresponding amide or lactam, wherein, when the aromatic compound (A1) alone is used as the catalyst, the solvent is at least one solvent selected typically from hydrocarbon solvents. The production process can yield amides or lactams simply in high yields without causing large amounts of by-products such as ammonium sulfate.