A fatty acid alkyl ester of the general formula I: ##STR00001## and acrolein are prepared by reacting a triglyceride of the general formula II: ##STR00002## wherein a) the triglyceride is reacted using an alcohol R'--OH in the presence of a catalyst to give said fatty acid alkyl ester and glycerol; and b) the glycerol is dehydrated catalytically to acrolein, wherein R is R.sub.1, R.sub.2 and R.sub.3, and R.sub.1, R.sub.2 and R.sub.3 are all the same or some are the same or all are different and are each a straight-chain or branched, and optionally mono- or polyunsaturated C.sub.10-C.sub.30-alkyl radical, and R' is a C.sub.1-C.sub.10-alkyl radical or a C.sub.3-C.sub.6-cycloalkyl radical.