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The functional composition principle is generalized by taking into account ofhistory of context change. Analysis of Peres' example shows hysteresis of valueassignments. It is shown that value assignments which depend on the history ofcontext change are possible in the case that the Hilbert space of state vectorsis finite dimensional.Comment: 22 pages. Errors in the previous proof of Proposition 5 were  corrected. This is the full version of "On Hysteresis of Value Assignments to  Observables during Changes of Context" in Foundations of Probability and  Physics - 4, eds. A. Yu. Khrennikov et al., AIP Conf. Proc. 889, 2007, pp.  422-42