We recently demonstrated that near-field scanning optical microscopy (NSOM) can be combined with fluorescence correlation spectroscopy (FCS) to reveal the kinetics of protein transport through a biological membrane under physiological conditions. The NSOM probe, an illuminated aperture, was placed some 10 nm above a nuclear pore complex in a freestanding nuclear membrane to measure the fluorescence intensity of labeled proteins moving in the transport channel. Since a NSOM aperture probe has a typical size of 30-80 nm and the intensity of the transmitted light decays exponentially with increasing distance to the aperture at a distance of only 10-25 nm, an ultra-small excitation volume for FCS is created. As a result of the steep intensity gradient along the axis of the transport channel, large fluorescence fluctuations can occur even for displacements of the fluorophore of only some 10 nm. Here we discuss in detail a simple model for the confined diffusion (CDM) of particles within a transport channel and derive an autocorrelation function for a corresponding NSOM-FCS measurement. Monte Carlo simulations confirm the analytic solution and are used to calculate the diffusional motion of particles with varying diffusion coefficient along the axis of the channel. It turned out that the simulated autocorrelation functions can be excellently fitted using the autocorrelation function of the CDM. Thus we found that the CDM is an adequate model even for the description of more complex diffusional motion in the channel as long as the related fit parameters are considered as effective values which are averaged over the real conditions in the transport channel.