We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.

This project has been supported by G.N.S.A.G.A. of INdAM - Rome (Italy), by MIUR of the Italian Government (Research Projects: PRIN "Real and complex manifolds: geometry, topology and harmonic analysis'', FIRB "Geometric function theory and differential geometry" and SIR "Analytic aspects in complex and hypercomplex geometry'').