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In a previous work we have introduced the concept of quasi-integrable quantumsystem. In the present one we determine sufficient conditions under which,given an integrable classical system, it is possible to construct aquasi-integrable quantum system by means of a quantization procedure based onthe symmetrized product of operators. This procedure will be applied toconcrete classes of integrable systems in two following papers.

Quantization of classical integrable systems. Part II: quantization of functions on Poisson manifolds