Summary: We consider a non-selfadjoint Dirac-type differential expression \[D(Q) y : = J_n \frac{d y}{d x} + Q(x) y,\] with a non-selfadjoint potential matrix \(Q \in L_{\operatorname{loc}}^1(\mathcal{I}, \mathbb{C}^{n \times n})\) and a signature matrix \(J_n = - J_n^{- 1} = - J_n^\ast \in \mathbb{C}^{n \times n}\). Here, \(\mathcal{I}\) denotes either the line \(\mathbb{R}\) or the half-line \(\mathbb{R}_+\). With this differential expression one associates in \(L^2(\mathcal{I}, \mathbb{C}^n)\) the (closed) maximal and minimal operators \(D_{\max}(Q)\) and \(D_{\min}(Q)\), respectively. One of our main results for the whole line case states that \(D_{\max}(Q) = D_{\min}(Q)\) in \(L^2(\mathbb{R}, \mathbb{C}^n)\). Moreover, we show that, if the minimal operator \(D_{\min}(Q)\) in \(L^2(\mathbb{R}, \mathbb{C}^n)\) is \(j\)-symmetric with respect to an appropriate involution \(j\), then it is \(j\)-selfadjoint. Similar results are valid in the case of the semiaxis \(\mathbb{R}_+\). In particular, we show that, if \(n = 2 p\) and the minimal operator \(D_{\min}^+(Q)\) in \(L^2(\mathbb{R}_+, \mathbb{C}^{2 p})\) is \(j\)-symmetric, then there exists a \(2 p \times p\)-Weyl-type matrix solution \(\Psi(z, \cdot) \in L^2(\mathbb{R}_+, \mathbb{C}^{2 p \times p})\) of the equation \(D_{\max}^+(Q) \Psi(z, \cdot) = z \Psi(z, \cdot)\). A similar result is valid for the expression (0.1) whenever there exists a proper extension \(\tilde{A}\) with \(\dim(\operatorname{dom} \tilde{A} / \operatorname{dom} D_{\min}^+(Q)) = p\) and nonempty resolvent set. In particular, it holds if a potential matrix \(Q\) has a bounded imaginary part. This leads to the existence of a unique Weyl function for the expression (0.1). The main results are proven by means of a reduction to the self-adjoint case by using the technique of dual pairs of operators. The differential expression (0.1) is of significance as it appears in the Lax formulation of the vector-valued nonlinear Schrödinger equation.