Starting from the hypothesis that the pion interacts with nucleons and hyperons only through intermediate fields, non-local covariant models of pion-nucleon, and pion-hyperon interactions can be obtained after formal elimination of the intermediate fields. First a simple mathematical model is discussed which admits exact solutions. This model has some formal features in common with the Pais-Uhlenbeck non-local theory but avoids the non definite energy difficulty. From this model a static nucleon-nucleon potential is obtained which exhibits a core effect in the central part and no divergence in the tensor part. Then a physical model is suggested in which the internal field is represented by a couple of K-mesons of opposite parity. A linear approximation of this model is equivalent to a non-local form factor theory of pion-nucleon pion-hyperon interactions of the Kristensen-Moller type in which the Fourier transform of the form factor is, however, of a class more general than that of the algebraic functions. A theory started from this form factor lagrangian exhibits general convergence features which are breafly discussed in appendix. In this linear approximation, relations between the K-nucleon-hyperon and pion-nucleon, pion-hyperon coupling constants, are obtained.