This study establishes maximum-efficiency architectures for heat- and work-regenerative gas turbine engines using a systematic irreversibility minimization approach. It considers engine architectures that employ two kinds of energy transfers: heat and work. It does not assume any cycle a priori (e.g., heat recuperative reactive Brayton cycle). Instead, the maximum-efficiency architecture is directly deduced from first principles. Not surprisingly, the optimal architecture has some conventional features such as regenerative heat transfer from post-expansion combustion products to post-compression air, and external heat transfer out during compression (intercooling). But in addition it has three non conventional features. First, unlike conventional heat recuperation heat is withdrawn between expansion turbine stages and transferred to post-compression air. Second, air is further compressed after heating. Third, compression is required to be part intercooled and part non-intercooled. (c) 2016 Elsevier Ltd. All rights reserved.