  In this paper we introduce a definition of the pre-Schwarzian and the
Schwarzian derivatives of any locally univalent harmonic mapping $f$ in the
complex plane without assuming any additional condition on the (second complex)
dilatation $\omega_f$ of $f$. Using the new definition for the Schwarzian
derivative of harmonic mappings, we prove analogous theorems to those by
Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the
univalence of harmonic mappings.
