We investigate heterotic string theory on special holonomy manifolds including exceptional holonomy G(2) and Spin(7) manifolds. The gauge symmetry is F-4 in a G(2) manifold compactification, and so(9) in a Spin(7) manifold compactification. We also study the cascade of the holonomies: so(8) superset of Spin(7) superset of G(2) superset of su(3) superset of su(2). The differences of adjoining groups are described by Ising, tricritical Ising, 3-state Potts and u(1) models. These theories are essential for spacetime supersymmetries and gauge group enhancements. As concrete examples, we construct the modular invariant partition functions and analyze their massless spectra for G(2) and Spin(7) orbifolds. We obtain the relation between topological numbers of the manifolds and multiplicities of matters in specific representations. (C) 2002 Elsevier Science B.V. All rights reserved.