A cleaning or detergent composition comprising a) one or more surfactant components selected from the group consisting of: (i) alkoxylated fatty alcohols of the general formula R 1 O(C n H2 n O) x H, wherein the composition comprises two different alkoxylated fatty alcohols, a mixture of R 1a O(C 2 H 4 O) 5-7 H and R O(C 2 H 4 O) 12-16 H, wherein R and R may be the same or different and represent a linear or branched alkyl or alkenyl residue with 15 to 20 carbon atoms, preferably with 16 to 18 carbon atoms, (ii) fatty acids of the general formula R 2 CO 2 M and (iii) anionic surfactants, or mixtures thereof, wherein R 1 and R 2 independently represent a linear or branched alkyl or alkenyl residue with 8 to 22 carbon atoms, n ranges from 1 to 5 and preferably is 2 or 3, x represents the degree of alkoxylation ranging from 5 to 25, and M represents hydrogen or an alkali metal ion; b) one or more alkalinity sources, c) water, and d) 5 to 30 wt.-%, based on the whole composition, of a phosphate substitute comprising: i) a water-soluble copolymer comprising at least two different aliphatic unsaturated monomer units and having a calcium carbonate dispersing capacity of at least 150 mg CaCO 3 /g copolymer and ii) a multidentate chelating agent comprising three to six complexing groups per molecule and forming water-soluble complexes with Ca 2+ - ions, wherein the ratio of the copolymer to the chelating agent is in the range of greater than 1: 1 to 3: 1 (wt.-%/wt.-% based on the whole composition) and the composition is free from any phosphates, silicates and cellulose-based compounds. a) one or more surfactant components selected from the group consisting of: (i) alkoxylated fatty alcohols of the general formula R 1 O(C n H2 n O) x H, wherein the composition comprises two different alkoxylated fatty alcohols, a mixture of R 1a O(C 2 H 4 O) 5-7 H and R O(C 2 H 4 O) 12-16 H, wherein R and R may be the same or different and represent a linear or branched alkyl or alkenyl residue with 15 to 20 carbon atoms, preferably with 16 to 18 carbon atoms, (ii) fatty acids of the general formula R 2 CO 2 M and (iii) anionic surfactants, or mixtures thereof, wherein R 1 and R 2 independently represent a linear or branched alkyl or alkenyl residue with 8 to 22 carbon atoms, n ranges from 1 to 5 and preferably is 2 or 3, x represents the degree of alkoxylation ranging from 5 to 25, and M represents hydrogen or an alkali metal ion; (i) alkoxylated fatty alcohols of the general formula R 1 O(C n H2 n O) x H, wherein the composition comprises two different alkoxylated fatty alcohols, a mixture of R 1a O(C 2 H 4 O) 5-7 H and R O(C 2 H 4 O) 12-16 H, wherein R and R may be the same or different and represent a linear or branched alkyl or alkenyl residue with 15 to 20 carbon atoms, preferably with 16 to 18 carbon atoms, (ii) fatty acids of the general formula R 2 CO 2 M and (iii) anionic surfactants, or mixtures thereof, wherein R 1 and R 2 independently represent a linear or branched alkyl or alkenyl residue with 8 to 22 carbon atoms, n ranges from 1 to 5 and preferably is 2 or 3, x represents the degree of alkoxylation ranging from 5 to 25, and M represents hydrogen or an alkali metal ion; b) one or more alkalinity sources, c) water, and d) 5 to 30 wt.-%, based on the whole composition, of a phosphate substitute comprising: i) a water-soluble copolymer comprising at least two different aliphatic unsaturated monomer units and having a calcium carbonate dispersing capacity of at least 150 mg CaCO 3 /g copolymer and ii) a multidentate chelating agent comprising three to six complexing groups per molecule and forming water-soluble complexes with Ca 2+ - ions, wherein the ratio of the copolymer to the chelating agent is in the range of greater than 1: 1 to 3: 1 (wt.-%/wt.-% based on the whole composition) and the composition is free from any phosphates, silicates and cellulose-based compounds. i) a water-soluble copolymer comprising at least two different aliphatic unsaturated monomer units and having a calcium carbonate dispersing capacity of at least 150 mg CaCO 3 /g copolymer and ii) a multidentate chelating agent comprising three to six complexing groups per molecule and forming water-soluble complexes with Ca 2+ - ions, wherein the ratio of the copolymer to the chelating agent is in the range of greater than 1: 1 to 3: 1 (wt.-%/wt.-% based on the whole composition) and the composition is free from any phosphates, silicates and cellulose-based compounds.