The main aim of this thesis is to present some new and recent results from the theory of non-Newtonian fluids. Such results refer to different motions of generalized second grade and Oldroyd-B fluids and ordinary Maxwell fluids. Generally, the constitutive equations for generalized non-Newtonian fluids are obtained from those of non-Newtonian fluids by replacing the time derivatives of an integer order by the so called Riemann-Liouville fractional operators. Chapter 1 and 2 contain introduction and basic preliminaries. In chapter 3, it is studied the rotational flow of a generalized second grade fluid between two infinite coaxial cylinders. The obtained solutions can be specialized to give the similar solutions for ordinary second grade and Newtonian fluids performing the same motion. Chapter 4 deals with the study of helical flow of generalized Oldroyd-B fluids in a single circular cylinder. Chapter 5 contains some remarkable results regarding the energetic balance for the flow of Maxwell fluid due to a constantly accelerating plate. Dissipation, the power of shear stress and boundary layer thickness have been determined analytically and are discussed.