This paper investigates the general and complete form of slope-deflection equations used in structural analysis. The word "complete" indicates that all the possible deformations (deflections and rotations) and all the strain energies (due to shear, direct stress and flexure) are included in the equations. The definitions, numbers, and relations of member constants are then discussed and the general equations for computing these constants are given. By neglecting the factors of minor importance, the general form is reduced to the usual slope-deflection equations. Some special forms of such equations which are useful in certain practical problems are also discussed briefly, such as the slope-deflection equations including the effect of direct stress on flexure and the slope-deflection equations of semi-rigid frames. Slope deflection equations for trussed bents are also presented.