This paper deals with the effect of radicals (in the Kurosh-Amitsur sense) on supplementary semilattice sums of rings as defined by J. Weissglass (Proc. Amer. Math. Soc., 39 (1973), 471-473). It is shown that if ℜ is a strict, hereditary radical class, then ℜ (R)= Σ α∈ Ω ℜ (R α) for every supplementary semilattice sum R= Σ α∈ Ω R α with finite Ω. If ℜ is an A-radical ciass or the generalized nil radical class, the same conclusion holds with the finiteness restriction removed. On the other hand, if ℜ (Σ α∈ Ω R α)= Σ α∈ Ω ℜ (R α) for all finite Ω, then ℜ is strict and satisfies (∗) R∈ ℜ⇒ the zeroring on the additive group of R belongs to ℜ, a condition satisfled by both hereditary strict and A-radical classes.