  The study of the relation between the Weierstrass inducing formulae for
constant mean curvature surfaces and the completely integrable euclidean
nonlinear sigma-model suggests a connection among integrable sigma -models in a
background and other type of surfaces. We show how a generalization of the
Weierstrass representation can be achieved and we establish a connection with
the Weingarten surfaces. We suggest also a possible generalization for
two-dimensional surfaces immersed in a flat space R^8 with Euclidean metric.
