The following generalization of the Cauchy-Riemann system is being considered. This system, denoted by (H), is closely related to the hyperbolic metric onRn+1+. EmbeddingRn+1+into the Clifford algebra Cn, the powers xk(k∈N) yield solutions of (H). Also, compositions of solution with Möbius transformations inRn+1+lead to solutions of (H). General rules associating new solutions to given ones are finally being investigated.