Summary: Fuzzy Galois connections were introduced by R. Bělohlávek [Math. Log. Q. 45, 497-504 (1999; Zbl 0938.03079)]. The structure considered there for the set of truth values is a complete residuated lattice, which places the discussion in a “commutative fuzzy world”. What we do in this paper is dropping down the commutativity, getting the corresponding notion of Galois connection and generalizing some results obtained by Bělohlávek. The lack of the commutative law in the structure of truth values makes it appropriate to deal with a conjunction where the order between the terms of the conjunction counts, gaining thus a temporal dimension for the statements. In this “non-commutative world”, we have not one, but two implications. As a consequence, a Galois connection will not be a pair, but a quadruple of functions, which is in fact two pairs of functions, each function being in a symmetric situation to its pair. Stating that these two pairs are compatible in some sense, we get the notion of strong \(L\)-Galois connection, a more operative and prolific notion, repairing the “damage” done by noncommutativity.