Abstract: In this talk we define an approximate notion of centralizers and commutators. We establish basic properties, such as the three-subgroup lemma, for the almost commutators and centralizers of ind-definable subgroups which are well-known facts in the ordinary case. With these results we are able to generalize Hall's nilpotency criteria and a theorem due to Fitting to FC-nilpotent subgroups of so called MC-group. These are groups with a chain condition on centralizers up to finite index whose crucial property in this context is that the almost centralizer of any subgroup is definable. They appear naturally in the field of model theory, i.e. any group with a simple theory has this property.