A method for reducing total suspended solids (TSS) and turbidity in wastewater from olive oil mill, wineries, piggeries, cowsheds, slaughterhouses, fruit and vegetable processing industry, soy or coffee bean industry, bromine industry, dairy effluents or saline effluents, wherein said method comprises the treatment of the wastewater with: (a) a nanocomposite consisting of (ai) anchoring particles based on zeolites, diatomaceous earth, powdered activated carbon or aluminium or magnesium silicate clay minerals selected from sepiolite, palygorskite, smectite, montmorillonite, vermiculite, hectorite, laponite, bentonite, or saponite, and (aii) one or more polymers, at least one of said polymers being a polyelectrolyte polymer that is a polycationic polymer selected from poly(diallyl dimethylammonium) chloride (poly-DADMAC), cationic polyacrylamide, poly(dimethylamine-co-epichlorohydrin-co-ethylenediamine) (PDEE), poly[bis(2-chloroethyl) ether-alt-1,3-bis[3-(dimethylamino)propyl]urea] quaternized (PQ2), poly [(3-methyl-1-vinylimidazolium chloride)-co-(1-vinylpyrrolidone)] (PMVV), chitosan, poly [(2-ethyldimethylammonioethyl methacrylate ethyl sulfate)-co-(1-vinylpyrrolidone)], quaternized hydroxyethylcellulose ethoxylate, and guar gum, or a polyanionic polymer selected from a poly(methyl vinyl ether-alt-maleic anhydride) copolymer (PMVE) or a poly(acrylamide-co-acrylic acid) copolymer (PAM), and (b) a bridging agent selected from (bi) a polycationic polymer with low charge density selected from polyquaternium 2 (PQ2), polyquaternium 15 (PQ15), polyquaternium 45 (PQ45), or polyquaternium 47 (PQ47), or (bii) a polyanionic polymer with low charge density selected from poly(acrylamide-co-acrylic acid), acrylamide/sodium acryloyldimethyltaurate copolymer, or acrylamide/sodium acryloyldimethyltaurate/acrylic acid terpolymer, whereby said polyelectrolyte polymer (aii) of the nanocomposite (a) neutralizes the charged colloidal particles suspended in said wastewater while anchoring them to the anchoring particles (ai) of the nanocomposites to form small flocks of the nanocomposites bound to the wastewater colloidal particles, and the bridging agent (b) bridges the small flocks to form large aggregates, thus enhancing their precipitation. (a) a nanocomposite consisting of (ai) anchoring particles based on zeolites, diatomaceous earth, powdered activated carbon or aluminium or magnesium silicate clay minerals selected from sepiolite, palygorskite, smectite, montmorillonite, vermiculite, hectorite, laponite, bentonite, or saponite, and (aii) one or more polymers, at least one of said polymers being a polyelectrolyte polymer that is a polycationic polymer selected from poly(diallyl dimethylammonium) chloride (poly-DADMAC), cationic polyacrylamide, poly(dimethylamine-co-epichlorohydrin-co-ethylenediamine) (PDEE), poly[bis(2-chloroethyl) ether-alt-1,3-bis[3-(dimethylamino)propyl]urea] quaternized (PQ2), poly [(3-methyl-1-vinylimidazolium chloride)-co-(1-vinylpyrrolidone)] (PMVV), chitosan, poly [(2-ethyldimethylammonioethyl methacrylate ethyl sulfate)-co-(1-vinylpyrrolidone)], quaternized hydroxyethylcellulose ethoxylate, and guar gum, or a polyanionic polymer selected from a poly(methyl vinyl ether-alt-maleic anhydride) copolymer (PMVE) or a poly(acrylamide-co-acrylic acid) copolymer (PAM), and (b) a bridging agent selected from (bi) a polycationic polymer with low charge density selected from polyquaternium 2 (PQ2), polyquaternium 15 (PQ15), polyquaternium 45 (PQ45), or polyquaternium 47 (PQ47), or (bii) a polyanionic polymer with low charge density selected from poly(acrylamide-co-acrylic acid), acrylamide/sodium acryloyldimethyltaurate copolymer, or acrylamide/sodium acryloyldimethyltaurate/acrylic acid terpolymer, <EOS>