The nilpotent minima are important t-norms in fuzzy logic and fuzzy reasoning. Two interesting formal systems—nilpotent minimum logic NM and L ∗ -based on nilpotent minima have been proposed and have been intensively studied. In this paper, their equivalence is pointed out. Moreover, coincidence of two related algebraic structures—NM- and R 0-algebras—is also proved. In addition, we give an equivalent form of involutive monoidal t-norm-based logic IMTL.