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Using a general, second-order, nonlocal formalism (Ganguli et al., 1985, 1988, 1994), we find that multiple Inhomogeneous Energy-Density Driven (IEDD) nonlocal eigenmodes with comparable growth rates are possible for a given set of parameters. This is in contrast to local modes and to most of the nonlocal modes, where the "the ground state" is usually most unstable. This finding suggests a possible explanation of the broadband and spiky spectrum of IEDD waves seen in laboratory experiments (Koepke et al., 1994, 1995; Amatucci et al., 1994; Carroll et al., 1996) and in Particle-In-Cell simulations (Nishikawa et al., 1988, 1990). We develop a simplified model and use it to predict a qualitative dependence of these multiple eigenstates on plasma and shear parameters. This second-order, nonlocal, linear formalism and its asymptotic limits are introduced and used to study the IEDD effects on ion-cyclotron, ion-acoustic and drift modes. We study special properties of the IEDD modes such as temperature ratio dependence, temperature anisotropy and multi-component effects. We generalize the second-order nonlocal formalism to higher orders and include velocity-gradient terms in some limiting cases of the second-order dispersion equation. We study the influence of (1) the shear parameters and (2) geometrical effects on the plasma equilibrium state and its development. A detailed description and theoretical interpretation of the West Virginia University Q-machine and the Naval Research Laboratory Space Physics Simulation Chamber experiments are presented. Finally, we review the main results of 2D Particle-In-Cell simulations for related instabilities. Possible applications of our results to space conditions are discussed.