Nanocryotrons have emerged in recent years as a candidate for superconducting electronics. Their inherent spiking behavior and robustness against magnetic fields make them suitable devices for implementing reliable low-power systems at cryogenic temperatures. Although some proof-of-concept devices based on nanocryotrons have been demonstrated, the lack of reliable standard cells that combine memory and logic functions has hindered the design of larger circuits. In this work, a logic family based on this technology is proposed. This family constitutes a complete set of cells that combine sequential and combinatorial functions. In particular, the set of gates and memory cells offers a sound basis for the design of any finite state machine.