In this paper a formalism, called perturbational crystal orbital theory, is proposed and examined. This formalism is based on a recent formulation of the perturbational molecular orbital theory in matrix form, and could be considered as an extension of it to periodic lattices. The perturbational crystal orbital theory is applied to the study of the energy band changes due to geometrical and electronegative perturbations of a 1D lattice. For these cases, the exact results are compared with those obtained by applying the proposed formalism up to second order, and a discussion of those results is carried out.