This paper presents upper bounds on the masses of supersymmetric particles based on the "naturalness" criterion. These bounds are derived as functions of the top quark mass and are used to test or disprove the idea of low-energy supersymmetry, as implemented in supergravity models. The bounds strongly differentiate between weakly interacting superparticles, such as charginos and neutralinos, which are lighter than 100-200 GeV, and strongly interacting ones, such as gluinos and squarks, which can be heavier than 1 TeV. The paper analyzes the electroweak symmetry breaking scale, or the Z-boson mass, as a function of the most general parameters of the theory. This function must include all one-loop renormalization group improved effects. The top quark mass plays a crucial role in determining the appropriate gauge symmetry breaking. The parameters of the theory control the masses of the various supersymmetric partners of the standard particles. The analysis shows that a consistent range of parameters allows arbitrarily heavy superpartners while keeping the Z-boson mass fixed. However, this requires an unnatural tuning among the physical parameters of the theory. To avoid this tuning, the paper imposes a condition that limits the percentage variation of any parameter to a maximum value. This condition leads to upper bounds on all dimensional parameters of the theory and therefore on all superparticle masses. These bounds are shown in figures for a specific value of the tuning parameter. The paper discusses the bounds on the parameters of the minimal supergravity model, including the soft breaking terms that determine the classical vacuum of the theory and drive the spontaneous breaking of supersymmetry. The bounds on the dimensionful parameters of the theory are related to the bounds on the different supersymmetric particles. The paper concludes that the results provide a sound basis for testing or disproving supergravity models. The bounds on weakly interacting particles, such as charginos and neutralinos, are of particular significance. These results suggest that e+e- colliders may be the most efficient machines to discover supersymmetry. The "naturalness" criterion is emphasized as a way to avoid quadratic divergences in the Higgs squared mass. If no supersymmetric particle is found below the given limits, the case for low-energy supersymmetry becomes significantly weakened.This paper presents upper bounds on the masses of supersymmetric particles based on the "naturalness" criterion. These bounds are derived as functions of the top quark mass and are used to test or disprove the idea of low-energy supersymmetry, as implemented in supergravity models. The bounds strongly differentiate between weakly interacting superparticles, such as charginos and neutralinos, which are lighter than 100-200 GeV, and strongly interacting ones, such as gluinos and squarks, which can be heavier than 1 TeV. The paper analyzes the electroweak symmetry breaking scale, or the Z-boson mass, as a function of the most general parameters of the theory. This function must include all one-loop renormalization group improved effects. The top quark mass plays a crucial role in determining the appropriate gauge symmetry breaking. The parameters of the theory control the masses of the various supersymmetric partners of the standard particles. The analysis shows that a consistent range of parameters allows arbitrarily heavy superpartners while keeping the Z-boson mass fixed. However, this requires an unnatural tuning among the physical parameters of the theory. To avoid this tuning, the paper imposes a condition that limits the percentage variation of any parameter to a maximum value. This condition leads to upper bounds on all dimensional parameters of the theory and therefore on all superparticle masses. These bounds are shown in figures for a specific value of the tuning parameter. The paper discusses the bounds on the parameters of the minimal supergravity model, including the soft breaking terms that determine the classical vacuum of the theory and drive the spontaneous breaking of supersymmetry. The bounds on the dimensionful parameters of the theory are related to the bounds on the different supersymmetric particles. The paper concludes that the results provide a sound basis for testing or disproving supergravity models. The bounds on weakly interacting particles, such as charginos and neutralinos, are of particular significance. These results suggest that e+e- colliders may be the most efficient machines to discover supersymmetry. The "naturalness" criterion is emphasized as a way to avoid quadratic divergences in the Higgs squared mass. If no supersymmetric particle is found below the given limits, the case for low-energy supersymmetry becomes significantly weakened.