ABSTRACT AST-9318745 KOUPELIS, Theodoros A two-dimensional analytic model for outflows (jets) in galaxies will be developed. It will be used in part on the approach of first finding the integrals of motion of the magnetohydrodynamic (MHD) equations describing the flow. The development of a one-dimensional analytic model in which the system of the ideal MHD equations is projected onto the jet axis (the narrow-jet model) will be completed. Using these models an investigation of the relative importance of different physical mechanisms on the collimation and continuous acceleration of outflows from a variety of astrophysical objects will be conducted. The first objective of this project is to find the allowed ranges of values of the physical parameters at the jet origin (e.g., magnetic field strength, density, etc.) for an outflow to be possible, and to study its evolution as the physical conditions close to its source change continuously. The goal is to study the physics of the regions at the origin of jets by using the information provided by observations of the outflow along its length. The second objective is to examine the effects of different pressure distributions and magnetic field strengths in the medium surrounding the outflow on its collimation and evolution. The goal is to study the propagation and stability properties of outflows in different environments. Using appropriate values for the parameters of interest or, when available, the limits imposed by the observations of specific outflows and the environments, the theoretical results will be compared with numerical simulations, and with outflows from active nuclei, neutron stars, and prostars. ***