A dynamical system (X, T) is F-transitive if for each pair of open and non-empty subsets U and V of X, N (U,V) = {n ∈ Z+: U ∩ T−nV ≠ Ø} ∈ F-where F is a collection of subsets of Z+ that is hereditary upward. (X, T) is F-mixing if (X×X, T×T) is F-transitive. For a subset S of Z+, (x, y ∈ X×X is S-proximal if lim inf Sn →+∞ d (Tn (x), Tn (y)) = 0 and the S-proximal cell PS (x) is the set of points that are S-proximal to x ∈ X. We show that if (X, T) is F-mixing, then for each S ∈ kF (the dual family of F) and x ∈ X, PS (x) is a dense Gδ subset of X, and when (X, T) is minimal and Fis a filter the reciprocal is true. Moreover, other conditions under which the reciprocal is true are obtained. Finally the structure of proximal cells for F-mixing systems is discussed, and a newand simpler proof of the Xiong-Yang theorem is presented.