The Path Computation Element Communication Protocol (PCEP) provides mechanisms for Path Computation Elements (PCEs) to perform path computations in response to Path Computation Clients (PCCs) requests. Although PCEP explicitly makes no assumptions regarding the information available to the PCE, it also makes no provisions for PCE control of timing and sequence of path computations within and across PCEP sessions. This document describes a set of extensions to PCEP to enable stateful control of MPLS-TE and GMPLS LSPs via PCEP.