In [2], the first two authors generalized the concept of $n$-isoclinism to the class of all pairs of groups. We extend that notion to $\nu$-isologism and study the details of this notion. In addition, it is shown that every pair of groups is $\nu$-isologic with a quotient irreducible pair of groups. Finally, as an application, we drive some inequalities for the Baer-invariant of a pair of groups.