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We investigate instability and reversibility within Hybrid Monte Carlosimulations using a non-perturbatively improved Wilson action. We demonstratethe onset of instability as tolerance parameters and molecular dynamics stepsizes are varied. We compare these findings with theoretical expectations andpresent limits on simulation parameters within which a stable and reversiblealgorithm is obtained for physically relevant simulations. Results ofoptimisation experiments with respect to tolerance prarameters are alsopresented.Comment: RevTeX, Some results here were presented at Vielat 99, Vienna,  Austria, Sept 1999 22 Pages, 10 figures, to be submitted to PR

Instability in the molecular dynamics step of a hybrid Monte Carlo algorithm in dynamical fermion lattice QCD simulations