  In this paper we study the deformation theory of submanifolds characterized
by a system of differential forms and provide a criterion for deformations of
such submanifolds to be unobstructed. We apply this deformation theory to
special Legendrian submanifolds in Sasaki-Einstein manifolds. In general,
special Legendrian deformations have the obstruction. However, we show that the
deformation space of special Legendrian submanifolds is the intersection of two
larger smooth deformation spaces of different types. We also prove that any
special Legendrian submanifold admits smooth deformations, which are not
special Legendrian deformations, given by harmonic $1$-forms.
