We consider universal algebras
(
S
;
{
∧
}
∪
E
)
(S;\{ \wedge \} \cup E)
in which E is a set of endomorphisms of the semilattice
(
S
;
∧
)
(S; \wedge )
. It is proved in this paper that such an algebra is equationally compact iff (i) every nonempty subset of S has an infimum, (ii) every up-directed subset of S has a supremum, (iii) for every
s
∈
S
s \in S
and every up-directed family
(
d
i
)
({d_i})
in S the equality
s
∧
∨
d
i
=
∨
s
∧
d
i
s \wedge \vee {d_i} = \vee s \wedge {d_i}
holds, (iv) for each
f
∈
E
,
f
(
∧
s
i
)
=
∧
f
(
s
i
)
f \in E,f( \wedge {s_i}) = \wedge f({s_i})
holds for every family
(
s
i
)
({s_i})
in S, and (v) for each
f
∈
E
,
f
(
∨
d
i
)
=
∨
f
(
d
i
)
f \in E,f( \vee {d_i}) = \vee f({d_i})
holds for every up-directed family
(
d
i
)
({d_i})
in S. In addition, it is shown that every equationally compact algebra of this type is a retract (algebraic) of a compact, Hausdorff, 0-dimensional topological one. These results reduce to known ones for semilattices without additional structure.