Three theorems are presented which give the, generally non-unique, representation of a k-vector function in terms of a k - 1-vector function and a k + 1-vector function, in ultrahyperbolic Clifford analysis with general signature (p,q). When specialized to the case (p,q) = (1,3) and k = 2, these theorems have a direct application in the domain of electromagnetism. The specialized theorems characterize: (i) the decomposition of an electromagnetic field in terms of an electric field and a magnetic field, (ii) the representation of an electromagnetic field in terms of potential fields and (iii) the representation of an electromagnetic field in terms of source fields.