Electrophoretic NMR (eNMR) and pulsed-field-gradient NMR (PFG-NMR) methods were used to study transport processes in situ and in a chemically resolved manner in the electrolyte of an experimental direct methanol fuel cell (DMFC) setup, constituted of several layers of Nafion 117. The measurements were conducted at room temperature for membranes fully swollen by methanol–water mixtures over a wide concentration interval. The experimental setup and the experimental protocol for the eNMR experiments are discussed in detail. The magnitude of the water and methanol self-diffusion coefficients show a good agreement with previously published data while the ratio of the two self-diffusion coefficients may indicate an imperfect mixing of the two solvent molecules. On the molecular level, the drag of water and methanol molecules by protons is roughly of the same magnitude, with the drag of methanol molecules increasing with increasing methanol content. The electro-osmotic drag defined on mass-flow basis increased for methanol from a low level with increasing methanol concentration while that of water remained roughly constant.