Self-aligning ball bearings are constructed with the inner ring and ball assembly contained within an outer ring that has a spherical raceway. This construction allows the bearing to tolerate a small angular misalignment resulting from deflection or improper mounting. The self-aligning ball bearing has two rows of balls and a common concave sphered raceway in the outer ring. The bearing is consequently self-aligning and insensitive to angular misalignments of the shaft relative to the housing. Self-aligning ball bearings with extended inner ring are designed for less demanding applications using commercial grade shafting. The special bore tolerance allows easy mounting and dismounting. When two self-aligning ball bearings with extended inner ring are used to support a shaft, they should be positioned so that the inner ring slots either face each other, or are at the outboard positions of the bearings. If this is not the case, the shaft is axially located in one direction only.