The notion of an $\mathcal L$-valued (i.e. fuzzy) algebraic closure system over a set is defined, where $\mathcal L$ is a complete lattice. If $\mathcal L$ is algebraic, then an $\mathcal L$-valued algebraic closure system determines an algebraic lattice. For a given algebra $\mathcal A=(A,F)$, the set $\overline{S_{\mathcal L}(A)}$ of its $\mathcal L$-valued subalqebras is an $\mathcal L$-valued algebraic closure system over $A$ (and thus $\overline{(S_{\mathcal L}(\mathcal A)} ,\subseteq)$ , is an algebraic lattice), if $\mathcal L$ is complete, and consists of compact elements only.