Monthly averaged surface erythemal solar irradiance (UV-Ery) for local noon from 1960 to 2100 has been derived using radiative transfer calculations and projections of ozone, temperature and cloud change from 14 chemistry climate models (CCM), as part of the CCMVal-2 activity of SPARC. Our calculations show the influence of ozone depletion and recovery on erythemal irradiance. In addition, we investigate UV-Ery changes caused by climate change due to increasing greenhouse gas concentrations. The latter include effects of both stratospheric ozone and cloud changes. The derived estimates provide a global picture of the likely changes in erythemal irradiance during the 21st century. Uncertainties arise from the assumed scenarios, different parameterizations - particularly of cloud effects on UV-Ery - and the spread in the CCM projections. The calculations suggest that relative to 1980, annually mean UV-Ery in the 2090s will be on average ~12 % lower at high latitudes in both hemispheres, ~3 % lower at mid latitudes, and marginally higher (~1 %) in the tropics. The largest reduction (~16 %) is projected for Antarctica in October. Cloud effects are responsible for 2-3 % of the reduction in UV-Ery at high latitudes, but they slightly moderate it at mid-latitudes (~1 %). The year of return of erythemal irradiance to values of certain milestones (1965 and 1980) depends largely on the return of column ozone to the corresponding levels and is associated with large uncertainties mainly due to the spread of the model projections. The inclusion of cloud effects in the calculations has only a small effect of the return years. At mid and high latitudes, changes in clouds and stratospheric ozone transport by global circulation changes due to greenhouse gases will sustain the erythemal irradiance at levels below those in 1965, despite the removal of ozone depleting substances. At northern high latitudes (60°-90°), the projected decreases in cloud transmittance towards the end of the 21st century will reduce the yearly average surface erythemal irradiance by ~5 % with respect to the 1960s.