We　consider　a　subclass　of　the　nonlinear　ABS　algorithm　for　solving　nonlinear　systems　of　equations　corresponding　to　a　generalization　of　the　Voevodin　method　for　linear　systems　which　includes　all　conjugate　gradient　type　methods.　A　local　Q-order　convergence　theorem　is　obtained　under　only　the　standard　conditions　on　the　mapping,　without　additional　conditions　on　the　parameters　defining　the　class.　©　1992,　Taylor　&　Francis　Group,　LLC.　All　rights　reserved.