Let

$\overline{M}$ be a Riemannian manifold equipped with an almost contact metric structure

$(\varphi ,\xi ,\eta ,g)$. A submanifold

$M$ of

$\overline{M}$ is said to be pseudo-slant if the structure vector field

$\xi $ is tangent to

$M$ everywhere, and if there exist two subbundles

${D}_{1}$ and

${D}_{2}$ of the tangent bundle

$TM$ of

$M$ such that

$TM$ decomposes orthogonally into

$TM={D}_{1}\oplus {D}_{2}\oplus \mathbb{R}\xi $,

$\varphi {D}_{1}$ is a subbundle of the normal bundle of

$M$, and there exists a real number

$0\le \theta <\pi /2$ such that for each nonzero vector

$X\in {D}_{2}$ the angle between

$\varphi X$ and

${D}_{2}$ is equal to

$\theta $. The authors derive some equations for certain tensor fields and investigate the integrability of some distributions on pseudo-slant submanifolds for the special case that the almost contact metric structure is Sasakian.