  This paper considers a generalization of the existing concept of parallel
(with respect to a given connection) geometric objects and its possible usage
as a suggesting rule in searching for adequate field equations in theoretical
physics. The generalization tries to represent mathematically the two-sided
nature of the physical objects, the {\it change} and the {\it conservation}.
The physical objects are presented mathematically by sections $\Psi$ of vector
bundles, the admissible changes $D\Psi$ are described as a rsult of the action
of appropriate differential operators $D$ on these sections, and the
conservation propertieis are accounted for by the requirement that suitable
projections of $D\Psi$ on $\Psi$ and on other appropriate sections must be
zero. It is shown that the most important equations of theoretical physics obey
this rule. Extended forms of Maxwell and Yang-Mills equations are also
considered.
