The three-terminal quantum-well-light-emitting transistors (QW-LETs) possess appealing characteristics, including multipath bidirectional electrical and optical inputs/outputs, transistor functionalities, and picosecond recombination lifetimes. This article presents the inaugural demonstration of electro-optical sequential logic circuits—first implementations of set-reset (SR) latches. These two latches feature both electrical and optical connectivities through a three-terminal QW-LET platform. Universal gates, such as NOR and NAND logic gates, have been manufactured and showcased, exhibiting accurate logic functionalities. Additionally, we propose two electro-optical SR latches based on NOR and NAND logic gates—the electro-optical registers, serving as fundamental building blocks for more intricate optoelectronic field-programmable gate arrays. The monolithically integrated QW-LET platform holds the potential to offer a comprehensive range of potent building blocks for optoelectronic chips and high-performance optoelectronic computing.