SYNOPSIS. Locomotor adaptations in actinopterygian fishes are described for (a) caudal propulsion, used in cruising and sprint swimming, acceleration, and fast turns and (b) median and paired fin propulsion used for slow swimming and in precise maneuver. Caudal swimming is subdivided into steady (time independent) and unsteady (time dependent acceleration and turning) locomotion. High power caudal propulsion is the major theme in actinopterygian swimming morphology because of its role in predator evasion and food capture. Non-caudal slow swimming appears to be secondary and is not exploited before the Acanthopterygii. Optimal morphological requirements for unsteady swimming are (a) large caudal fin and general body area, (b) deep caudal peduncle, often enhanced by posterior dorsal and anal fins, (c) an anterior stabilizing body mass and\or added mass, (d) flexible body and (e) large ratio of muscle mass to body mass. Optimal morphological requirements for steady swimming are (a) high aspect ratio caudal fin, (b) narrow caudal peduncle, (c) small total caudal area, (d) anterior stabilizing body mass and added mass, and (e) a stiff body. Small changes in morphology can have large effects on performance. Exclusive morphological requirements for steady versus unsteady swimming are partially overcome using collapsible fins, but compromises remain necessary. Morphologies favoring unsteady performance are a recurring theme in actinopterygian evolution. Successive radiations at chondrostean, halecostome and teleostean levels are associated with modifications in the axial and caudal skeleton. Strength of ossified structures probably limited maximum propulsion forces early in actinopterygian evolution, so that specializations for fast cruising (carangiform and thunmform modes) followed structural advances especially in the caudal skeleton. No such limits apply to eel-like forms which consequently recur in successive actinopterygian radiations. Slow swimming using mainly non-caudal propulsion probably first occurred among neopterygians in association with reduced and neutral buoyancy. Slow swimming adaptations can add to and extend the scope of caudal swimming, but specialization is associated with reduced caudal swimming performance. Marked exploitation of slow swimming opportunities does not occur prior to the anterodorsal location of pectoral and pelvic girdles and the vertical rotation of the base of the pectoral fin, as found in the Acanthopterygii.