The combination of far-field and near-field scanning optical microscopy (NSOM) with a position (line) and wavelength dependent detection allow us to observe the fluorescence form points away from the excitation spot. This contrasts with confocal illumination/detection and with fluorescent imaging of uniform illumination, the two commonly used fluorescence measurement modes. We discuss the origins of the nonlocal emission and argue that the results can be used to measure the exciton diffusion length in these two-dimensional materials. In particular, we study transition metal dichalcogenides. We use near-field second harmonic generation (SHG) with NSOM detection of the mode-locked femtosecond laser pulse generated signals.