A novel approach is presented for the qualitative analysis of the dynamic behavior of homogeneous azeotropic distillation columns of finite length. The methodology can be used to study the dynamic behavior of steady-state column profiles after perturbations. The key concept is to study the interaction of changes in the total column holdup composition and the shape of the column profile, This allows one to qualitatively determine if the profiles are locally stable or unstable. It is shown that the stability of the steady states is dominantly governed by the external mass balance around the column. This is highlighted by studying the case of infinite internal flows where the internal dynamics of the column become infinitely fast while the external dynamics remain at a slow time scale. The analysis of the local stability of column profiles presented in this work will be extended to construct bifurcation diagrams in the accompanying paper (Dorn, C.; Morari, M. Ind. Eng. Chem. Res, 2002, 4 1, XXXX).