A nondiagrammatic formulation of the analytical first derivative of the coupled-cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree-Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(1) = X for first-order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non-perturbation-dependent set of equations can be solved instead. This and the first-order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.