The article discusses the influence of the thickness of the wear-resistant layer of the Zr-ZrN-(Zr,Al,Si)N nanolayer composite coating on the values of residual stress and the nature of coating wear. The study focused on coatings with wear-resistant layer thicknesses of 2.0, 4.3, 5.9, and 8.5 µm, deposited using filtered cathodic vacuum arc deposition (FCVAD) technology. The X-ray diffraction (XRD) method based on the anisotropy of the elasticity modulus was used to find the values of the residual stress. The nature of the formation of interlayer delamination under the influence of residual compressive stress was studied using a scanning electron microscope (SEM). When the wear-resistant layers had a thickness of 2.0–5.9 μm, tensile stress formed, which decreased with an increase in the thickness of the coating. When the thickness of a wear-resistant layer was 8.5 μm, compressive stress formed. Under the action of compressive stress, periodic interlayer delamination formed, with a pitch of about 10 binary nanolayers. A mathematical model is proposed to describe the nature of the formation of interlayer delamination under the influence of compressive residual stress, including in the presence of a microdroplet embedded in the coating structure.