using these objects was to show [@BMMS; @BS] that it is possible to expand a one-parameter family of diffeomorphism, at orden $n$, using Lie derivatives with respect to a finite number $n$ of vector fields. Knight diffeomorphisms constitute an elegant formulation of this kind of expansions. In order to apply these ideas to our case, we can think of translating the idea of knight diffeomorphims from the one-parameter to the two-parameter case. We have studied this question and we have found that in the two–parameter case there are several ways of formulating knight diffeomorphisms, and they lead to different formal expansions of a two-parameter family of diffeomorphisms. Actually, we have found that some of these formulations can be inconsistent in the sense that the differential operators that come out from them do not satisfy the Leibnitz rule. Then, we cannot associated to any of these operators a vector field whose Lie derivative will describe the action of that operator. Despite of these facts, we find that the main goal for introducing knight diffeomorphisms can be achieved in the two-parameter case. That is, we can still expand a two-parameter family of diffeomorphisms, at order $n$, using Lie derivatives with respect to 