Authors’ summary: We construct the generalized Darboux transformation with arbitrary functions at time \(t\) for the AKNS equation with self-consistent sources (AKNSESCS) which, in contrast with the Darboux transformation for the AKNS equation, provides a non-auto-Bäcklund transformation between two AKNSESCSs with different degrees of sources. The formula for \(N\)-times repeated generalized Darboux transformations is proposed. By reduction the generalized Darboux transformation with arbitrary functions at time \(t\) for the nonlinear Schrödinger equation with self-consistent sources (NLSESCS) is obtained and enables us to find the dark soliton, bright soliton and position solutions for NLS\(^+\)ESCS and NLS\(^-\)ESCS. The properties of these solutions are analysed.