Let VBn, respectively WBn denote the virtual, respectively welded, braid group on n-strands. We study their commutator subgroups VB n = [VBn,VBn] and, WB n = [WBn,WBn], respectively. We obtain a set of generators and defining relations for these commutator subgroups. In particular, we prove that VB n is finitely generated if and only if n = 4, and WB n is finitely generated for n = 3. Also, we prove that VB 3/VB 3 = Z3 Z3Z3Z 8,VB 4/VB 4 = Z3Z3Z3,WB 3/WB 3 = Z3Z3Z3Z,WB 4/WB 4 = Z3, and for n = 5 the commutator subgroups VB n andWB n are perfect, i.e. the commutator subgroup is equal to the second commutator subgroup.