Let \(G\) be a noncompact exceptional simple Lie group with finite center, and \(K\) a maximal compact subgroup of \(G\). Assume that \(\text{ rank} G = \text{ rank} K\) and \(G/K\) is not a Hermitian symmetric space. Let \(\text{Lie}_{\mathbf C} G\) be the complexification of the Lie algebra of \(G\). By A. W. Knapp [Representation Theory 1, 1-24 (1997; Zbl 0887.22019)] the \((\text{Lie}_{\mathbf C} G, K)\)-module \(A_{q}(\lambda)\) was defined. For \(\text{Lie}_{\mathbf C} G\neq \text{ E}_8\), the authors determine the Langlands parameters for the natural irreducible constituent of \(A_{q}(\lambda)\) with the only exception when \(\lambda \) is outside the weakly good range.