Processes for preparing conjugated fatty acid glycerides comprising: (a) isomerizing a fatty acid lower alkyl ester corresponding to the general formula (I) in the presence of a basic catalyst at a temperature of from 100 to 160° C., to form a conjugated fatty acid lower alkyl ester: R1CO—OR2  (I) wherein R1CO represents an acyl radical having from 16 to 22 carbon atoms and at least two carbon-carbon unsaturations and R2 represents an alkyl radical having from 1 to 4 carbon atoms; and (b) transesterifying the conjugated fatty acid lower alkyl ester with glycerol to form a conjugated fatty acid glyceride, wherein a lower alkanol corresponding to the general formula R2OH is formed, wherein R2 is as defined above, and the lower alkanol is continuously removed from the transesterification reaction; are described.