  Let $1\leq p\leq q\leq\infty.$ Being motivated by the classical notions of
the Gelfand--Phillips property and the (coarse) Gelfand--Phillips property of
order $p$ of Banach spaces, we introduce and study different types of the
Gelfand--Phillips property of order $(p,q)$ (the $GP_{(p,q)}$ property) and the
coarse Gelfand--Phillips property of order $p$ in the realm of all locally
convex spaces. We compare these classes and show that they are stable under
taking direct product, direct sums and closed subspaces. It is shown that any
locally convex space is a quotient space of a locally convex space with the
$GP_{(p,q)}$ property. Characterizations of locally convex spaces with the
introduced Gelfand--Phillips type properties are given.
