We prove that an act X over a completely simple semigroup \(S=\mathcal{M}\left(G,I,\Lambda ,P\right)\) is congruence-simple (i.e., it has no nontrivial congruences) if and only if one of the following conditions holds: (1) |X| = 1; (2) |X| = 2 and |XS| = 1; (3) X = {z1, z2}, where z1 and z2 are zeros; (4) X ≅ R/ρ, where R is a minimal right ideal of the semigroup S and ρ is a maximal proper congruence of the right ideal R, which is considered as an act over S. We describe these congruences.
