This paper centers around two basic problems of topological coincidence
theory. First, try to measure (with help of Nielsen and minimum numbers) how
far a given pair of maps is from being loose, i.e. from being homotopic to a
pair of coincidence free maps. Secondly, describe the set of loose pairs of
homotopy classes. We give a brief (and necessarily very incomplete) survey of
some old and new advances concerning the first problem. Then we attack the
second problem mainly in the setting of homotopy groups. This leads also to a
very natural filtration of all homotopy sets. Explicit calculations are carried
out for maps into spheres and projective spaces
