Reflection High Energy Electron Diffraction (RHEED) oscillations under arsenic and gallium-controlled Molecular Beam Epitaxy (MBE) growth conditions have been used to measure the sticking and desorption coefficients of As2 and As4. The coefficients are obtained from measurements of the arsenic incorporation rates. Comparisons are made with measurements obtained from desorption rates using modulated beam mass spectroscopy. The transition from gallium to arsenic-controlled growth is observed to occur after excess gallium atoms accumulate on the surface. The maximum intrinsic arsenic sticking coefficients occur when the maximum number of gallium atoms can be incorporated for a given arsenic flux. The intrinsic maximum arsenic sticking coefficients are found to be 0.75 and 0.50 for As2 and As4, respectively. During galliumcontrolled growth, the arsenic sticking coefficients are independent of substrate temperature as long as the sticking coefficient of gallium is equal to one. However, a temperature dependent maximum gallium-controlled arsenic sticking coefficient exists. It can be measured by the maximum Ga to As4 flux ratio that produces specular film surfaces. During gallium-controlled growth, the Ga to As flux ratios are shown to be equal to the gallium-controlled arsenic sticking coefficients. The activation energy for arsenic desorption during arsenic-controlled growth conditions was measured as -0.50 eV for independent As4 and As2 incident fluxes. During gallium-controlled growth with incident As4 fluxes, an activation energy for arsenic desorption of -0.70 eV was measured for the maximum gallium-controlled arsenic sticking coefficients.