I will present an approach to Steinberg groups in categories of groups having commutator relations with respect to a family of root subgroups. It gives a unified frame work for the classical linear and unitary Steinberg groups. The latter are examples of Steinberg groups associated with root graded Jordan pairs. Excluding some low rank cases, these groups are centrally closed (as it should be).

The talk is based on joint work with Ottmar Loos which is partially supported by NSERC.