Process for producing acrolein, comprising the following steps: (a) dehydrating an aqueous glycerol phase G1 in an acrolein reaction region to give an aqueous acrolein reaction phase; (b) at least partially separating the aqueous acrolein reaction phase into an acrolein-rich acrolein phase and a residual phase R1 that is depleted in acrolein compared to the acrolein phase, wherein the residual phase R1 comprises glycerol, water and residues other than glycerol and water; (c) recirculating at least part of the residual phase R1 to step (a); wherein i) at least one of these residues is separated off from a glycerol phase G2 comprising glycerol, water and residues other than glycerol and water, and the purified glycerol phase G2 obtained in this way is fed directly to the acrolein reaction region, or ii) at least one of the residues other than glycerol and water is separated off from a mixed phase M1, obtained by mixing a glycerol phase G2, comprising glycerol, water and residues other than glycerol and water, with the acrolein-depleted residual phase R1, and the purified mixed phase M1 obtained in this way is fed to the acrolein reaction region, wherein, in addition to the purified glycerol phase G2 or the purified mixed phase M1, a further glycerol phase G3 is fed to the acrolein reaction region, wherein the glycerol phase G3 has a higher glycerol content than the glycerol phase G2, and wherein the glycerol phase G3 has a lower salt content than the glycerol phase G2 and wherein the glycerol phase G3 has a lower content of organic compounds other than glycerol than the glycerol phase G2, and wherein the glycerol phase G3 is obtained as a distillate in the distillation of crude glycerol obtained in the cleavage or transesterification of triglycerides and at least part of the bottom product obtained in the distillation of the crude glycerol passes through a salt separator and is subsequently fed back to the distillation of the crude glycerol. (a) dehydrating an aqueous glycerol phase G1 in an acrolein reaction region to give an aqueous acrolein reaction phase; (b) at least partially separating the aqueous acrolein reaction phase into an acrolein-rich acrolein phase and a residual phase R1 that is depleted in acrolein compared to the acrolein phase, wherein the residual phase R1 comprises glycerol, water and residues other than glycerol and water; (c) recirculating at least part of the residual phase R1 to step (a); wherein i) at least one of these residues is separated off from a glycerol phase G2 comprising glycerol, water and residues other than glycerol and water, and the purified glycerol phase G2 obtained in this way is fed directly to the acrolein reaction region, or ii) at least one of the residues other than glycerol and water is separated off from a mixed phase M1, obtained by mixing a glycerol phase G2, comprising glycerol, water and residues other than glycerol and water, with the acrolein-depleted residual phase R1, and the purified mixed phase M1 obtained in this way is fed to the acrolein reaction region, i) at least one of these residues is separated off from a glycerol phase G2 comprising glycerol, water and residues other than glycerol and water, and the purified glycerol phase G2 obtained in this way is fed directly to the acrolein reaction region, or ii) at least one of the residues other than glycerol and water is separated off from a mixed phase M1, obtained by mixing a glycerol phase G2, comprising glycerol, water and residues other than glycerol and water, with the acrolein-depleted residual phase R1, and the purified mixed phase M1 obtained in this way is fed to the acrolein reaction region,