This paper reports theoretical and experimental work on the transport of space‐charge‐dominated relativistic electron beams in a racetrack betatron with cusp focusing. High‐efficiency propagation of 550‐keV, 280‐A beams through a complex optical system consisting of two 180° arcs with 36 focusing cells and a straight section was observed. More than 90% of the injected beam was captured and transported through the 7‐m system. The experiments resolved several recent problems of beam injection and trapping in the machine and showed that electron beam transport at the space‐charge limit is possible in a curved cusp array despite strong axial variations of focusing forces. We encountered no problems with the transitions between curved and straight focusing sections. The experiments demonstrated good beam containment in a cusp array with mixed focusing cell geometries as long as the axially averaged focusing force was the same for all cells. The ability to use long cells is a critical feasibility issue for other planned injection experiments into a closed racetrack geometry.