Some properties and characterizations for abundant semigroups with generalised quasiadequate transversals are explored. In such semigroups, an interesting property [?a,b ? Re1S, VSo(a) VSo (b) 0 (a) = (b)] is investigated thus the concept of refined quasi-adequate transversals, short, RGQA introduced. It shown that real common generalisations both orthodox adequate in case. Finally, by means tw...