The uptake dynamics of HCl by single sulfuric acid microdroplets under stratospheric conditions is investigated. The droplets are typically 30-70 mu m in diameter and weakly charged so that they can be stored in an electrodynamic trap. The gas uptake of the droplets is monitored either by measuring their size by angle resolved Mie- scattering patterns or by electrostatic balancing of the droplets in the trap. At low temperatures and high sulfuric acid concentration (T < 190 K for 48 wt % H2SO4 and T ( 195 K for 56 wt % H2SO4, respectively), liquid-phase diffusion inside the droplet is the rate-limiting step in the overall uptake process. In this regime, the diffusion coefficients D-liq of HCl in supercooled sulfuric acid solutions are found to increase strongly with temperature and H2O concentration. The results are discussed with respect to diffusion models that have been proposed recently. In contrast, at higher temperatures and lower sulfuric acid concentrations (30-40 wt % H2SO4, 185-207 K) gas-phase diffusion with subsequent accommodation/dissolution at the liquid surface determines the observed uptake velocity. A new method to deduce accommodation coefficients alpha is proposed.