We report a combined experimental and theoretical study dedicated to analyze the N 1s core-level binding energies (CLBE) in N-doped carbon nanotubes (N-CNTs). X-ray photoelectron spectroscopy (XPS) data are obtained from N-CNT samples synthesized using the chemical vapor deposition technique. Extensive density functional theory (DFT) calculations are performed on various model single- and double-walled N-CNTs where N 1s CLBEs are determined using Koopman's theorem. However, we also present additional calculations within the (Z + 1) approximation to analyze the role of final-state effects. From XPS data up to 2 at% of N content was found in our samples and the high resolution analysis of the N 1s line shows, according to previous experimental results, that N species exist in CNTs as graphitic, pyrrolic, pyridinic, and molecular configurations. However, peak decomposition is characterized by five broad Gaussian curves that overlap considerably among them, having different widths and heights, implying a more complex distribution of N atoms within the structures. DFT calculations performed on model N-CNTs reveal a strong dependence of N 1s CLBE values and their shifts on the local atomic environment. Different types of graphitic N cover an energy range of 3 eV, while various configurations for pyridinic, pyrrolic, and molecular species reveal a dispersion in their energy values of 5.7, 2.7, and 5.2 eV, respectively. The previous distributions of theoretical CLBEs also strongly overlap, implying that some peaks in the XPS spectra must be understood as composite signals where the signals of different N defects coexist. We find, in agreement with the experimental data, that freestanding molecular nitrogen and (weakly interacting) encapsulated N₂ within the hollow core of model CNTs have very similar CLBEs. Furthermore, we predict that chemisorbed N₂ on defective regions of the nanotube walls has N 1s binding energy values that are considerably larger when compared to encapsulated N₂, thus making possible their identification. In contrast to previous reports, we find a nontrivial dependence between CLBEs and the local electronic occupation at N sites. The assignment of spectral details in the XPS data to well-defined N-defects on CNTs is not straightforward and needs to be more deeply analyzed.