The algebra of bicomplex numbers and the corresponding bicomplex holomorphic functions are well known ([1] and others). The hyperbolic bicomplex numbers were used by Dominic Rochon in different aspects (for instance [2]). The algebra of double‐complex numbers (in the sense of [3]) gives a parallel treatement closely related with the classical theory of two complex variables (to see [4]). The double‐complex holomorphicity and its fundamental equations were studied in [5] and [6]. In this paper we consider hyperbolic double‐complex functions. The corresponding hyperbolic analogous of the double‐complex Cauchy‐Riemann system and the double‐complex Laplacian are obtained. Some perspectives are described.