for the UIR spaces of the SU(3) subgroup. The matrix elements of the generators between the canonical basis vectors of the principal degenerate series of the SL(3, C) UIR spaces have been given QY Bose in the forms of the analytic continuation of the finite representations of the SL(3, C) group. 2l With the group expansion procedure, Mukunda has investigated the canonical bases of both principal degenerate and nondegenerate series of the SL(3, C) UIR's. 8l His representation space is just those of the SU(3) X T 8 UIR's, where the matrix elements of the SL (3, C) generators, given as the polynomial functions of the SU(3) X T 8 generators, are calculated. In the present pap.er we investigate the principal degenerate series of the SL(3, C) UIR's in order to describe the parts of the internal excitations of hadrons corresponding to the creation of the quarks and antiquarks in the frame work of the dynamical group approach, by which we discuss the mass levels of the hadro~ towers labeled with definite spin, parity (and C-parity) and the parameters d and p of the SL(3, C) UIR's in a succeeding paper. 4l By making use of the Bose operators, we give the UIR's as those of the Lie algebra of the generators of the infinitesimal SL (3, C) transformations. We construct the -representation space of the principal degenerate series from the Bose-F ock space !}{ defined by the, Bose operators ai and btk(i, k=l, 2, 3) and the vector I0),5l where the SL (3, C) generators are given as the simple bilinear forms of the