Concrete containing supplementary cementitious materials as, e.g. fly-ash (FA) or blast-furnace slag (BFS) is more vulnerable to carbonation than ordinary Portland cement concrete. In order to know whether carbonation-initiated corrosion is a risk within the life span of the concrete structure, the carbonation depth after several years (e.g. 50 years) is mostly predicted based on accelerated carbonation tests on young concrete specimens. However, these predictions do not take into account the positive effect of the continuing hydration of slag and fly-ash particles over a longer time. In this study, accelerated carbonation tests (10 vol.% of CO2) were performed on concrete specimens containing different amounts of blast-furnace slag (slag-to-binder ratios of 50%, 70% and 85%) after different curing times (1, 3, 6 or 18 months). Based on these tests, a new method, which takes into account the effect of the ongoing hydration, is described in order to predict the carbonation depth of these special types of concrete over a long time more realistically. The tests revealed that, although BFS concrete has a lower carbonation resistance than OPC concrete, the depth of carbonation at the end of the concrete's life (50 years) can still be acceptable in normal environments.