On the set
P
k
∗
$\begin{array}{}
\displaystyle
P_k^*
\end{array}$
of partial functions of the k-valued logic, we consider the implicative closure operator, which is the extension of the parametric closure operator via the logical implication. It is proved that, for any k ⩾ 2, the number of implicative closed classes in
P
k
∗
$\begin{array}{}
\displaystyle P_k^*
\end{array}$
is finite. For any k ⩾ 2, in
P
k
∗
$\begin{array}{}
\displaystyle P_k^*
\end{array}$
two series of implicative closed classes are defined. We show that these two series exhaust all implicative precomplete classes. We also identify all 8 atoms of the lattice of implicative closed classes in
P
3
∗
$\begin{array}{}
\displaystyle
P_3^*
\end{array}$
.