In this paper we show that if D is a valued F-central division algebra such that its residue division ring is a field, then each soluble-by-finite subgroup of its multiplicative group is soluble with derived length at most 3. We also prove that in some special cases the above bound for the length of the derived series is at most 2. Finally, using some examples we show that if the the residue division ring is not a field then the above resuklts are not true.