We consider the composition "$\circ$" of fuzzy binary relations on the set $\overline{C_w(A)}$ of weak fuzzy congruence relations on the given algebra $A$, using the complete lattice $L$. (Weak fuzzy congruence relations are defined for groupoids in [1], and it was proved in [2] that $\overline{(C_w(A)},\leqslant)$ is a complete lattice, having as a homomorphic image the lattice of all fuzzy subalgebras of $A$). We prove that, provided that $L$ is Infinitely distributive, $\overline{(C_w(A)},\circ)$ is a semilattice iff all weak fuzzy congruence relations on $A$ are permutable. Permutability, on the other hand, does not imply the equality $\bar\rho\circ\bar\theta=\bar\rho\vee\bar\theta$ in the lattice $\overline{(C_w(A)},\leqslant)$. Here we give the necessary and sufficent conditions for that equality, and we describe the connection between the operations $\circ$ and $\vee$ in all other cases.