In this paper, a three-dimensional almost Kenmotsu manifold M 3 satisfying the generalized (κ, µ)-nullity condition is investigated. We mainly prove that on M 3 the following statements are equivalent: (1) M 3 is φ-symmetric; (2) the Ricci tensor of M 3 is cyclic-parallel; (3) the Ricci tensor of M 3 is of Codazzi type; (4) M 3 is conformally flat with scalar curvature invariant along the Reeb vector field; (5) M 3 is locally isometric to either the hyperbolic space H 3 (−1) or the Riemannian product H 2 (−4) × R.