Three types of double sweep methods for solving the two-point boundary value pro-blems of difference equations are discussed. The forward sweep procedures in these me-thods are the same, but the backward sweep procedures are different. In the first typemethods, some relations for solutions are set up in the backward sweep by using only theboundary conditions at one point as in the forward sweep. In the second type methodsthese relat ons are set up by using also the relations obtained in the forward sweep. In thethird type methods, after the forward sweep some relations for solutions are set up byusing difference equations and the relations obtained in the forward sweep. Stsbility theorems for methods of these three types are proved by using directly thel~2-well conditionedness of the two-point boundary value problems, without requiring thediagonal dominance property.