In the late 1950s, the Soviet Air Force was seeking a jet-powered replacement for its fleet of piston-engined trainers, and this requirement was soon broadened to finding a trainer aircraft that could be adopted in common by Eastern Bloc air forces. Aero's response, the prototype XL-29 designed by Z. Rublič and K. Tomáš first flew on 5 April 1959, powered by a British Bristol Siddeley Viper engine. The second prototype was powered by the Czech-designed M701 engine, which was used in all subsequent aircraft.

The basic design concept was to produce a straightforward, easy-to-build and operate aircraft. Simplicity and ruggedness were stressed with manual flight controls, large flaps and the incorporation of perforated airbrakes on the fuselage sides providing stable and docile flight characteristics, leading to an enviable safety record for the type. The sturdy L-29 was able to operate from grass, sand or unprepared fields. Both student pilot and instructor had ejection seats, and were positioned in tandem, under separate canopies with a slightly raised instructor position.

In 1961, the L-29 was evaluated against the PZL TS-11 Iskra and Yakovlev Yak-30 and emerged the winner. Poland chose to pursue the development of the TS-11 Iskra anyway, but all other Warsaw Pact countries adopted the Delfin under the agreements of COMECON.