A coated cutting tool consisting of a substrate and a hard material coating, the substrate being selected from cemented carbide, cermet, ceramics, cubic boron nitride (cBN), polycrystalline diamond or high-speed steel, wherein the hard material coating comprises a (Ti,AI)N layer stack of alternately stacked (Ti,AI)N sub-layers, the layer stack having the following characteristics: - the overall atomic ratio of Ti:AI within the (Ti,AI)N layer stack is within the range from 0.33:0.67 to 0.67:0.33; - the total thickness of the (Ti,AI)N layer stack is within the range from 1 μm to 20 μm; - each of the individual (Ti,AI)N sub-layers within the (Ti,AI)N layer stack of alternately stacked (Ti,AI)N sub-layers has a thickness within the range from 0.5 nm to 50 nm; - each of the individual (Ti,AI)N sub-layers within the (Ti,AI)N layer stack of alternately stacked (Ti,AI)N sub-layers being different in respect of the atomic ratio Ti:Al than an immediately adjacent (Ti,AI)N sub-layer; - over the thickness of the (Ti,AI)N layer stack perpendicular to the substrate surface the content of Al increases and the content of Ti decreases from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate to the interface of the (Ti,AI)N layer stack arranged in the direction towards the outer surface of the coating; - over the thickness of the (Ti,AI)N layer stack perpendicular to the substrate surface the residual stress σ decreases from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate to the interface of the (Ti,AI)N layer stack arranged in the direction towards the outer surface of the coating by an amount of at least 150 MPa to at most 900 MPa, whereby the residual stress σ is measured by X-ray diffraction applying the sin 2 Ψ method based on the (2 0 0) reflection; - the residual stress σ within a portion of a thickness of at least 100 nm to at most 1 μm within the (Ti,AI)N layer stack from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate is within the range of from 0 MPa to +450 MPa - the difference between the absolute amounts of the residual stresses σ of (i) the portion of a thickness of at least 100 nm to at most 1 μm within the (Ti,AI)N layer stack from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate and of (ii) the material arranged immediately underneath, which is either the surface of the substrate or a hard material layer arranged between the substrate and the (Ti,AI)N layer stack, is ≤ 400 MPa; - the residual stress σ is measured as described in the description - the overall atomic ratio of Ti:AI within the (Ti,AI)N layer stack is within the range from 0.33:0.67 to 0.67:0.33; - the total thickness of the (Ti,AI)N layer stack is within the range from 1 μm to 20 μm; - each of the individual (Ti,AI)N sub-layers within the (Ti,AI)N layer stack of alternately stacked (Ti,AI)N sub-layers has a thickness within the range from 0.5 nm to 50 nm; - each of the individual (Ti,AI)N sub-layers within the (Ti,AI)N layer stack of alternately stacked (Ti,AI)N sub-layers being different in respect of the atomic ratio Ti:Al than an immediately adjacent (Ti,AI)N sub-layer; - over the thickness of the (Ti,AI)N layer stack perpendicular to the substrate surface the content of Al increases and the content of Ti decreases from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate to the interface of the (Ti,AI)N layer stack arranged in the direction towards the outer surface of the coating; - over the thickness of the (Ti,AI)N layer stack perpendicular to the substrate surface the residual stress σ decreases from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate to the interface of the (Ti,AI)N layer stack arranged in the direction towards the outer surface of the coating by an amount of at least 150 MPa to at most 900 MPa, whereby the residual stress σ is measured by X-ray diffraction applying the sin 2 Ψ method based on the (2 0 0) reflection; - the residual stress σ within a portion of a thickness of at least 100 nm to at most 1 μm within the (Ti,AI)N layer stack from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate is within the range of from 0 MPa to +450 MPa - the difference between the absolute amounts of the residual stresses σ of (i) the portion of a thickness of at least 100 nm to at most 1 μm within the (Ti,AI)N layer stack from the interface of the (Ti,AI)N layer stack arranged in the direction towards the substrate and of (ii) the material arranged immediately underneath, which is either the surface of the substrate or a hard material layer arranged between the substrate and the (Ti,AI)N layer stack, is ≤ 400 MPa; - the residual stress σ is measured as described in the description