Stability equations that evaluate the elastic critical axial load of stepped columns under extreme and intermediate concentrated axial loads in any type of construction with sidesway totally inhibited, partially inhibited and uninhibited are derived in a classical manner. These equations can be utilized in the stability analysis of framed structures (totally braced, partially braced, and unbraced) with stepped columns with rigid, semirigid, and simple connetions. The proposed column classification and the corresponding stability equations overcome the limitations of current methods which are based on a classification of braced and unbraced columns. The proposed stability equations include the effects of: 1) semirigid connections; 2) step variation in the column cross section at the point of application of the intermediate axial load; and 3) lateral and rotational restraints at the intermediate connection and at the column ends. The proposed method consists in determining the eigenvalue of a $2{ imes}2$ matrix for a braced column at the two ends and of a $3{ imes}3$ matrix for a partially braced or unbraced column. The stability analysis can be carried out directly with the help of a pocket calculator. The proposed method is general and can be extended to multi-stepped columns. Various examples are include to demonstrate the effectiveness of the proposed method and to verify that the calculated results are exact. Definite minimum bracing criteria for single stepped columns is also presented.