An explicitly connected commutator expansion for the average value of an observable in the coupled-cluster theory is derived. Specifically, it is shown that the expectation value of an operator for the state Ψ, related to the Fermi vacuum Φ by the exponential Ansatz ψ = eT Φ, is expressed as a finite commutator series containing the cluster operator T and an auxiliary operator S, defined by a linear equation involving again a finite commutator series in T. The above result is applied to derive the explicitly connected commutator form of the order-by-order many-body perturbation theory (MBPT) expansion for the expectation values and density matrices. We also show how the commutator expansion derived by us can be used as a basis for size-extensive infinite-order summation techniques. An operator technique of eliminating the nonlocal, “off-energy shell” denominators from MBPT expressions is proposed and applied to obtain compact commutator formulas for the expectation values of one- and two-electron operators through the fourth and third order, respectively, and for the correlation energy through the fifth order of perturbation theory. © 1993 John Wiley & Sons, Inc.