  We prove that if $I$ is a monomial ideal with linear quotients in a ring of
polynomials $S$ in $n$ indeterminates and $\operatorname{depth}(S/I)=n-2$, then
$\operatorname{sdepth}(S/I)=n-2$ and, if $I$ is squarefree,
$\operatorname{hdepth}(S/I)=n-2$.
  Also, we prove that $\operatorname{sdepth}(S/I)\geq
\operatorname{depth}(S/I)$ for a monomial ideal $I$ with linear quotients which
satisfies certain technical conditions.
