The sheath dynamics of helium and hydrogen RF-discharges at 13.56 MHz in the GEC reference cell are studied by laser spectroscopic electric field measurements. In case of helium, the Stark splitting of the n = 11 Rydberg state is measured by LIF spectroscopy applied to metastable helium atoms in the 2s¹S₀ state. A novel laser spectroscopic technique in atomic hydrogen allows the sensitive measurements of electric fields down to about 10 V cm^-1. Two-dimensional space and time resolved results are presented. Sheath voltages, sheath ion and net charge densities and displacement current densities are directly derived from the measured electric fields. Under certain assumptions, also the electron conduction and ion current densities, the power dissipated in the discharge and the ion energy distribution function can be inferred. The experimental results show that the common step-model for the spatial electron distribution in the sheath is a reasonable approximation in the case of helium but is less appropriate in hydrogen. In the hydrogen RF-discharge, field reversal during the anodic phase of the applied voltage is observed and investigated in detail. A simple analytic model for the field reversal effect is developed that describes quantitatively the experimental results.