  Harmonic functions are natural generalizations of conformal mappings. In
recent years, a lot of work have been done by some researchers who focus on
harmonic starlike functions. In this paper, we aim to introduce two classes of
harmonic univalent functions of the unit disk, called hereditarily
$\lambda$-spirallike functions and hereditarily strongly starlike functions,
which are the generalizations of $\lambda$-spirallike functions and strongly
starlike functions, respectively. We note that a relation can be obtained
between this two classes. We also investigate analytic characterization of
hereditarily spirallike functions and uniform boundedness of hereditarily
strongly starlike functions. Some coefficient conditions are given for
hereditary strong starlikeness and hereditary spirallikeness. As a simple
application, we consider a special form of harmonic functions.
