Poly(yne)-platinum polymers having the structure-Pt(PBu3)2-C = C-C = C-Pt(PBu3)2-C = C-C6H4-C = C- have been prepared according to the prescription developed by Hagihara, Takahashi, et al. The orientational characteristics of these polymers in the lyotropic nematic mesophase (trichloroethylene) were studied in relation to their phase behavior. The volume fractions, v'p and v"p, in the coexisting isotropic and anisotropic mesophase were found to be around 0.29 and 0.43, respectively. These values tend to be slightly higher in the low molecular weight region. The molecular weight distributions remain practically identical between the two conjugate phases. The orientational order parameter S was determined for partially deuterated polymers in the lyotropic liquid crystalline state (v(p) = 0.4-0.6) by using the H-2 NMR technique. Experimental S-v(p) curves tend to increase more rapidly toward higher concentrations (i.e., concave upward), suggesting that the persistence of orientational correlation along the chain increases as a function of concentration. All these observations indicate that the polymer chain is considerably flexible. Experimental results were compared with those of theoretical calculations: a persistence length q = 13 nm was adopted from Teramoto et al.'s work. The phase equilibrium data are reasonably well reproduced by Flory's Kuhn-chain model, which however failed to predict correct values for S. The persistent-chain model of Khokhlov and Semenov somewhat overestimates the values of v'p and v"p, indicating the need of consideration for higher virial terms in the theory. Further elaborations are required in theories for a quantitative description of the S-v(p) relation.