  In a series of two papers we present the theoretical results of $\pi
N$/meson-baryon scattering in the Kadyshevsky formalism. In this paper the
results are given for meson exchange diagrams. On the formal side we show, by
means of an example, how general couplings, i.e. couplings containing multiple
derivatives and/or higher spin fields, should be treated. We do this by
introducing and applying the Takahashi-Umezawa and the Gross-Jackiw method. For
practical purposes we introduce the $\bar{P}$ method. We also show how the
Takashashi-Umezawa method can be derived using the theory of Bogoliubov and
collaborators and the Gross-Jackiw method is also used to study the
$n$-dependence of the Kadyshevsky integral equation. Last but not least we
present the second quantization procedure of the quasi particle in Kadyshevsky
formalism.
