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A simple unified procedure is applied to derive irreducible nonpolynominal representations for scalar-, vector-, skewsymmetric and symmetric second order tensor-valued anisotropic constitutive equations involving any finite number of vector variables and second order tensor variables. In the paper consisting of three parts, we consider all kinds of material symmetry groups as subgroups of the cylindrical group D_∞h. This paper, together with a previous work, covers all kinds of material symmetric groups of solids, except for the five cubic crystal classes and the two icosahedral quasicrystal classes. In this part, our concern is with all crystal classes and quasicrystal classes D_2mh, D_2m and C_2mν for all integers m ≥ 2.