This thesis titled "Study of Some Dark Energy and String Models in Certain Alternative Theories of Gravitation" consists of eight chapters and deals with the investigation of some spatially homogeneous and anisotropic cosmological models in the frame work of Brans-Dicke (1961) and Saez-Ballester (1986) scalar-tensor theories, Barber's (1982) second self-creation theory and f(R, T ) modified theory of gravity (Harko et al. 2011), which are viable alternatives to Einstein's theory of gravitation. The main aim of cosmology is to construct mathematical models of the universe and compare these models with the present day universe as observed by astronomers. A full picture should comprise both an inventory of the present matter content (including its spatial distribution) and an understanding of the dynamics governing past and future evolution of the universe as a whole. Technological advances have brought an increasing ability to gather enormous quantities of data to further our understanding.