We exhibit some classes of baric algebras over a field for which the Krull-Schmidt theorem, proved in the previous paper “Indecomposable baric algebras,” is valid. We prove also that the commutative duplicate of an indecomposable commutative baric algebra A such that A 2 = A is indecomposable. Two more examples of indecomposable baric algebras, relevant in genetics, are given: linked and independent loci.