A general scheme of constructing a canonical structure (i.e. Poisson bracket, canonical fields) in classical field theories is proposed. The theory is manifestly independent of the particular choice of an initial space-like surface in space-time. The connection between dynamics and canonical structure is established. Applications to theories with a gauge and constraints are of special interest. Several physical examples are given.Recently one of us W. Szczyrba, using the general theory elaborated in the present paper has obtained a natural symplectic structure for a set on Einstein metrics in General Relativity. These results will be submitted for publication in Commun. math. Phys.The authors would like to thank Proffessors K. Maurin and I. Birula-Biaϊynicki for lively interest in their work and fruitful discussions.We thank also very much Professor D. Simms for his deep comments which were very valuable for us during the preparation of the manuscript.Our special thanks are due to Professor J. Ehlers for many profound remarks and improvements of the final version of this paper.

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