The T78-A-2 was originally designed as a potential replacement for the Allison T56 turboprop in the Lockheed P-3A ASW aircraft. It was also adaptable to airborne early warning aircraft based on Navy carriers, for large transports, and other applications where long endurance or low fuel consumption was of prime importance.

The T78 incorporated a regenerator system that was intended to reduce specific fuel consumption at low power settings and, thus greatly extend long-range and "on station" capabilities. The basic principle of regeneration involved reclamation of turbine exhaust heat to increase the temperature of compressor discharge air, thus reducing the amount of fuel required for the most efficient engine operating temperature.

By the spring of 1965, Allison had run the T78 at up to 85% of rated power during a one-hour test. Testing continued for a short period, but the engine was not put into production. Apparently some people in the Navy were opposed to increasing time on station for the P-3 because of crew fatigue problems.