We discuss whether there is a realistic Technicolor model under the constraints of Oblique and Non-oblique corrections from the precision measurements. To satisfy t he constraint of oblique correct ion. a one-family Technicolor model without exact custodial symmetry was proposed by Appelquist and Terning. We construct effective Lagrangian including technimesolls for the one-family Technicolor model without exact custodial symmetry. Tree level contributions to oblique correction parameters and S and U due to spin 1 technimesons are computed with the effective Lagrangian. An isospin breaking term which is associated with technilepton vector mesons gives a negative contribution to the electroweak radiative correction parameter S due to mixing between I = 0 and I = 1 vector mesons.

To satisfy the constraint of non-oblique correction. Zbb vertex correction the effects of diagonal extended technicolor interaction was studied by Wu. By means of the effective lagrangian approach, we discuss the effects of extended technicolor(ETC) gauge interaction to the oblique and non-oblique corrections. It is shown that the T parameter is unacceptably large whentlie Zbb vertex correction and S parameter are consistent with the experiments in the ETC model. Hence, some difficulty is still remained in the ETC mechanism.