The purpose of this paper is to study Ricci semisymmetric paracontact metric manifolds satisfying ξ h = 0 ξ h=0 and such that the sectional curvature of the plane section containing ξ equals a non-zero constant c. Also, we study paracontact metric manifolds satisfying the curvature condition Q R = 0 Q cdot R=0, where Q and R are the Ricci operator and the Riemannian curvature tensor, respectively, and second order symmetric parallel tensors in paracontact metric manifolds under the same conditions. Several consequences of these results are discussed. © 2018 Walter de Gruyter GmbH, Berlin/Boston.