  In this note it is worked out a new set of Laplace-Like equations for
quaternions through Riemann-Cauchy hypercomplex relations otained earlier
\cite{BorgesZeMarcio}. As in the theory of functions of a complex variable, it
is expected that this new set of Laplace-Like equations might be applied to a
large number of Physical problems, providing new insights in the Classical
Theory Fields.
