The quantitative effects of molecular weight and concentrations of two phase-forming polymers-polyethylene glycol and crude dextran on the two phase extractive ethanol fermentation were investigated using a Box-Wilson central composite protocol. The regression model obtained was used in order to determine optimum compositions of aqueous two phase system. In the aqueous two phase extractive ethanol fermentation of Kluyueromyces fragilis CBS 1555 with Jerusalem artichoke juice, it was found from the regression model that the variables influenlcing on ethanol fermentation were PEG concentration, time, Dx concentration, and PEG molecular weight strongly in order. The interaction of PEG concentration and PEG molecular weight was also found, and the effect of PEG concentration decreased with increase in molecular weight of PEG. The ethanol concentration incresed with increase in molecular weight of PEG, and with decrease in concentration of PEG. In conolusion, maximum concentration of ethanol produced was obtained at the following compositions; PEG MW 20000, Dx concentration ranged from 4% to 5%, and PEG concentration ranged from 3% to 7%.