A description is given of the K-matrix formalism. The formalism, which
is normally applied to two-body scattering processes, is generalized
to production of two-body channels with final-state interactions. A mu
lti-channel treatment of production of resonances has been worked out
in the P-vector approach of Aitchison. An alternative approach, derive
d from the P-vector, gives the production amplitude as a product of th
e T-matrix for a two-body system and a vector Q specifying its product
ion. This formulation, called Q-vector approach here, has also been wo
rked out. Examples of practical importance are given.