A general scheme for the spin adaptation of open-shell coupled-cluster theory is presented, and the generalization to genuine multireference cases is briefly discussed. In our formulation the wave operator is parameterized such that it automatically commutes with the spin operators, and the correlated wave function is hence a spin eigenfunction provided the reference state is. We employ an exponential form for the wave operator, which is assumed to be normal ordered with respect to a closed-shell vacuum state. The excitation operators can be expressed in terms of generators of the unitary group, and the number of independent coefficients is only marginally larger than in the dosed-shell case : Open-shell orbitals occur both as creation and as annihilation operators. Using our formalism we are able to obtain spin-orbital based equations, which are expressed in terms of second quantized matrix elements of the similarity transformed Hamiltonian. The explicit form of the similarity transformed Hamiltonian generated by normal ordered exponential operators is presented in an accompanying paper [M. Nooijen, J. Chem. Phys. 104, 2638 (1996) preceding paper], and is crucial to the present formulation.