The present paper proposes a new turbo-rotary compound engine (TRCE) and an associated novel thermodynamic cycle. In this engine, shafts linking customary gas turbine engines components such as axial compressors and axial turbines are eliminated. Instead, two or multiple spools are lined up in series within the engine. In the front spool, partial admission rotary vane type turbines drive axial compressor stages. In the back spool, axial turbine stages drive partial admission rotary vane type compressors. Two air streams feed separately the customary turbo components and the rotary vane components, respectively. Accordingly, the primary high mass flow through the axial compressors and turbines is mainly responsible for the generation of net engine thrust and power, where as the secondary, low mass flow through the partial admission rotary components is mainly used to generate the internal energy required to power the axial compressor stages. The energy consumed internally by the engine is minimized because less input shaft power is needed for the rotary vane compressors and higher inlet temperatures and less cooling can be tolerated by the intermittent combustion rotary vane turbines. The result is a radical improvement in both efficiency and net power output. Aerothermodynamics and spool matching calculations comparing a T56-A14 core with a TRCE of similar size and compression ratio show that the new engine provides superior performance characteristics by increasing the net output work by 100% and decreasing the specific fuel consumption by 20%.