Nonclassical physical theories including uncontrollable (quantum and/or thermal) effects leading to the fluctuations of physical characteristics are discussed. The proposed concept of universality of uncertainty relations (URs) implies that the product of the fluctuations of conjugate quantities is related to their generalized correlation function describing correlations of two different types. It is shown that the Schrödinger URs, whose particular realizations is the Heisenberg UR in convenient quantum dynamics and Einstein UR in statistical thermodynamics and theory of Brownian movement, falls into this concept. A substantial advance in studying the energy - time UR is achieved. On the basis of the Schrödinger URs, the Mandelstam-Tamm concept of time uncertainty is generalized. This generalized concept is conclusive, does not give rise to singularities, and enables us to introduce the generalized energy - time UR and to determine an effective frequency, which is a universal characteristic of an open microsystem as a whole and is governed by macroscopic external conditions. The efficiency of this generalized energy - time UR is exemplified by applying it to typical models of finite and infinite motions in the microcosm. The effective frequency of a microsystem is shown to fluctuate for coherent states, which makes it possible to change the generalized energy - time UR to the equivalent energy - inverse effective frequency UR. It is shown that correlation between fluctuations in this UR coincides with that in statistical thermodynamics but qualitatively differs from (hat in the Heisenberg UR. The results open up new possibilities or further applying the universal Schrödinger URs in the consistent theory of nonclassical physics. Copyright © 2001 by MAIK "Nauka/Interperiodica" (Russia).