We show that quark operators of twist 3 contributing to the polarized nucleon structure function g2tw.3(x, Q2) decouple from the evolution equation for the quark-gluon operators of the same twist in two important limits,Nc→∞ and n→∞ (Nc is the number of colours and n refers to the nth moment of g2). The anomalous dimensions for the quark operators turn out to be always the lowest ones in the spectrum. Asymptotic behaviour of g2(x, Q2) in the region 1−xmuch less-than1 is derived. Results of an extensive numerical study of the spectrum of anomalous dimensions for QCD and for the Nc→∞ cases are presented.