The new epitaxial technologies of molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) have added astonishing possibilities to the fabrication of sophisticated semiconductor structures like GaAs-A1As superlattices and heterostructure layers. Progress in fine line lithography makes one-dimensional (1-D) structures feasible in the near future. The potential of these new synthetic materials for device applications are considerable. In this research effort, transport properties will be studied and the possible applications of 1-D semiconductor systems to high performance devices will be explored. The work is theoretical. The approach includes a theory of the dielectric function of quasi-1-D systems and the derivation of the collective modes of a 1-D electron gas. The transport theory is based on the semi-classical Boltzmann equation and special emphasis is given to the electron-polar optical phonon interaction and to inter-carrier scattering. The 1-D electron distribution function for low and high field transport will be obtained. The guideline of this investigation will be the analogy of 1-D structures with magnetotransport. For complex transport processes, simulation methods (Monte Carlo) will be developed.