A simple heat cascading regenerative sorption heat pump process with rejected or waste heat from a higher temperature chemisorption circuit ("HTCC") powering a lower temperature physisorption circuit ("LTPC") which provides a 30% total improvement over simple regenerative physisorption compression heat pumps when ammonia is both the chemisorbate and physisorbate, and a total improvement of 50% or more for LTPC having two pressure stages. The HTCC contains ammonia and a chemisorbent therefor contained in a plurality of canisters, a condenser-evaporator-radiator system, and a heater, operatively connected together. The LTPC contains ammonia and a physisorbent therefor contained in a plurality of compressors, a condenser-evaporator-radiator system, operatively connected together. A closed heat transfer circuit ("CHTC") is provided which contains a flowing heat transfer liquid ("FHTL") in thermal communication with each canister and each compressor for cascading heat from the HTCC to the LTPC. Heat is regenerated within the LTPC by transferring heat from one compressor to another. In one embodiment the regeneration is performed by another CHTC containing another FHTL in thermal communication with each compressor. In another embodiment the HTCC powers a lower temperature ammonia water absorption circuit ("LTAWAC") which contains a generator-absorber system containing the absorbent, and a condenser-evaporator-radiator system, operatively connected together. The absorbent is water or an absorbent aqueous solution. A CHTC is provided which contains a FHTL in thermal communication with the generator for cascading heat from the HTCC to the LTAWAC. Heat is regenerated within the LTAWAC by transferring heat from the generator to the absorber. The chemical composition of the chemisorbent is different than the chemical composition of the physisorbent, and the absorbent. The chemical composition of the FHTL is different than the chemisorbent, the physisorbent, the absorbent, and ammonia.