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In the present study the possibilities are investigated how the methodology o£ sciences, i. e., the theory of method can overcome the descriptive (empirical, intuitive) stage and become an exact science. Exact method may be defined by means of exact science, or exact science by means of exact method. If we use the former procedure, then the essential condition of making methodology more exact is to create a pure (really abstract) image of an ideal science which is deprived of fortuities of various provenience; this image must result from an analysis of the experience of scientists working in different fields and from its evaluation. An exact expression of the above pure image of science and its creation will be the next step. It is a common experinece that if some part of science or a whole scientific discipline cannot be built in an exact way with its own means, exact models are sought for it. In methodology, mathematical and formal systemic models may be taken into account. In such a way we obtain a set-theoretical, algebraic (structural), algorithmic, statistical, informational, cybernetic, strategic (game-theoretical), operationalistic and systemic model of science, methodology, and method. Each of these models brings also a certain conception of science and its method, so that by connecting them we obtain a complex picture of science and method. In the present study preparatory and consequential stages of rendering methodology more exact are differentiated. At the preparatory stage, the concept of science and method is understood intuitively empirically, but the individual procedures, e. g., analysis, induction, experiment, theory etc. are being expressed and, consequently, made more exact by means of set-, algebraic, ..., systemic concepts. At the consequential stage, science and method as a whole is understood from the standpoint of set..........of system. Each model has its „own“ logic (of set, algebraic, set-theoretical. . .) which may be built in a constructive or nonconstructive way and thus further different pictures of science and its method can be obtained. The set-theoretical and algebraic (structural) models of science and method are then analysed both the standpoint of the preparatory stage and from the standpoint of the consequential stage of the process of rendering he methodology of sciences more exact; attention is paid particularly to the problems connected with this process as far as induction is concerned.