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We give a classification of 3-family SO(10) and E_6 grand unification instring theory within the framework of conformal field theory and asymmetricorbifolds. We argue that the construction of such models in the heteroticstring theory requires certain Z_6 asymmetric orbifolds that include a Z_3outer-automorphism, the latter yielding a level-3 current algebra for the grandunification gauge group SO(10) or E_6. We then classify all such Z_6 asymmetricorbifolds that result in models with a non-abelian hidden sector. All modelsclassified in this paper have only one adjoint (but no other higherrepresentation) Higgs field in the grand unified gauge group. In addition, allof them are completely anomaly free. There are two types of such 3-familymodels. The first type consists of the unique SO(10) model with SU(2) X SU(2) XSU(2) as its hidden sector (which is not asymptotically-free at the stringscale). This SO(10) model has 4 left-handed and 1 right-handed 16s. The secondtype is described by a moduli space containing 17 models (distinguished bytheir massless spectra). All these models have an SU(2) hidden sector, and 5left-handed and 2 right-handed families in the grand unified gauge group. Oneof these models is the unique E_6 model with an asymptotically-free SU(2)hidden sector. The others are SO(10) models, 8 of them with an asymptoticallyfree hidden sector at the string scale.Comment: 35 pages, Revtex 3.0, one eps figure (to appear in Phys. Rev. D

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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