I introduce a class of string constructions based on asymmetric orbifo
lds leading to level two models. In particular, I derive in detail var
ious models with gauge groups E(6) and SO(10), including a four genera
tion E(6) model with two adjoint representations. The occurrence of mu
ltiple adjoint representations is a generic feature of the constructio
n. In the course of describing this approach, I will address the probl
em of twist phases in higher twisted sectors of asymmetric orbifolds.