The dictionary definition of stability as “Firmly established, not easily to be changed” immediately indicates the conflict between stability and maneuverability in aquatic locomotion. The present paper addresses several issues resulting from these opposing requirements. Classical stability theory for bodies moving in fluids is based on developments in submarine and airship motions. These have lateral symmetry, in common with most animals. This enables the separation of the equations of motion into two sets of 3 each. The vertical (longitudinal) set, which includes motions in the axial (surge), normal (heave) and pitching directions, can thus be separated from the lateral-horizontal plane which includes yaw, roll and sideslip motions. This has been found useful in the past for longitudinal stability studies based on coasting configurations but is not applicable to the analysis of turning, fast starts and vigorous swimming, where the lateral symmetry of the fish body is broken by bending motions. The present paper will also examine some of the aspects of the stability vs. maneuverability tradeoff for these asymmetric motions. An analysis of the conditions under which the separation of equations of motions into vertical and horizontal planes is justified, and a definition of the equations to be used in cases where this separation is not accurate enough is presented.