Axially symmetric cosmological models with cosmic string source are obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A113, 467, 1985). The models obtained give us axially symmetric geometric (Nambu) string, p-string and Reddy string (Astrophys. Space Sci. 286, 2003b) in Saez-Ballester theory. Some physical properties of the models are also discussed.

An exact Bianchi type-V perfect fluid cosmological model is obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra Manifold in case of β is a constant and it is shown that this cosmological model exists only in the case of Radiation Universe (ρ = 3p) if β is a function of 't' using negative constant deceleration parameter. Some physical and geometrical properties of these models are discussed.

Exact Bianchi type II, VIII and IX String cosmological models are obtained in the Saez-Ballester theory of gravitation. Some physical and geometrical properties of the models are studied.

Bermann (1983) [Nuovo Cimento B, 74, 182] obtained a cosmological model with the help of special law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. Here, we present Bianchi-I model with negative constant deceleration parameter in Brans-Dicke (1961) [Phys. Rev., 124, 925] theory in the presence of perfect fluid source with disordered radiation. Some physical properties of the model are also discussed.

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