A new class of spatially homogeneous Kantowski-Sachs string cosmological models with bulk viscosity in Nordtvedt (1970) general scalar-tensor theory of gravitation with the help of a special case proposed by Schwinger (1970) is obtained. In this paper we have presented anisotropic as well as isotropic cosmological models. Some important features of the models, thus obtained, have been discussed. These exact models are new and more general and represent not only the early stages of evolution but also the present universe. 1. Introduction Nordtvedt [1] proposed a general class of scalar-tensor gravitational theories in which the parameter of the BD theory is allowed to be an arbitrary (positive definite) function of the scalar field . This general class of scalar-tensor gravitational theories includes the Jordan [2] and Brans-Dicke [3] theories as special cases. Barker [4], Ruban and Finkelstein [5], Banerjee and Santos [6, 7], and Shanti and Rao [8, 9] are some of the authors who have investigated several aspects of Nordtvedt general scalar-tensor theory. Rao and Kumari [10] have discussed a cosmological model with negative constant deceleration parameter in this theory, and very recently Rao et al. [11] have obtained Kaluza-Klein radiating model in a general scalar-tensor theory of gravitation. The field equations of general scalar-tensor theory proposed by Nordtvedt are where is the Ricci tensor, is the scalar curvature, is the stress energy tensor of the matter, and comma and semicolon denote partial and covariant differentiation, respectively. Also, we have which is a consequence of the field equations (1). Beside the Bianchi type metrics, the Kantowski-Sachs [12] models are also describing spatially homogeneous universes. For a review of Kantowski-Sachs of metrics one can refer to MacCallum [13]. These metrics represent homogeneous but anisotropically expanding (or contacting) cosmologies and provide models where the effects of anisotropic can be estimated and compared with all well-known Friedmann-Robertson-Walker class of cosmologies. Wang [14] has obtained Kantowski-Sachs string cosmological model with bulk viscosity in general relativity. Kandalkar et al. [15] have discussed Kantowski-Sachs viscous fluid cosmological model with a varying . Kandalkar et al. [16] have obtained string cosmology in Kantowski-Sachs space-time with bulk viscosity and magnetic field. Rao et al. [17] have studied various Bianchi type string cosmological models in the presence of bulk viscosity. Recently Rao et al. [18] and Rao and Sireesha [19] have obtained Bianchi
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