The present invention relates to methods for the production of .omega.-3 and/or .omega.-6 fatty acids in oleaginous yeast. Thus, desaturases and elongases able to catalyze the conversion of linoleic acid (LA) to .gamma.-linolenic acid (GLA); .alpha.-linoleic acid (ALA) to stearidonic acid (STA); GLA to dihomo-.gamma.-linoleic acid (DGLA); STA to eicosatetraenoic acid (ETA); DGLA to arachidonic acid (ARA); ETA to eicosapentaenoic acid (EPA); DGLA to ETA; EPA to docosapentaenoic acid (DPA); and ARA to EPA have been introduced into the genome of Yarrowia for synthesis of ARA and EPA.