  The prolongation structure of a two-by-two problem is formulated very
generally in terms of exterior differential forms on a standard representation
of Pauli matrices. The differential system is general without making reference
to any specific equation. An integrability condition is provided which gives by
construction the equation to be investigated and whose components involve the
structure constants of an SU(2) Lie algebra. Along side this, a related,
different kind of prolongation, a type of Wahlquist-Estabrook prolongation,
over a closed differential ideal is discussed and some applications are given.
