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With nanotextured surfaces and interfaces increasingly being encountered in technological and biomedical applications, there is a need for a better understanding of frictional properties involving such surfaces. Here we report friction measurements of several nanostructured surfaces using an Atomic Force Microscope (AFM). These nanostructured surfaces provide well defined model systems on which we have tested the applicability of Amontons' laws of friction. Our results show that Amontonian behaviour is observed with each of the surfaces studied. However, no correlation has been found between measured friction and various surface roughness parameters such as average surface roughness (R-a) and root mean squared (rms) roughness. Instead, we propose that the friction coefficient may be decomposed into two contributions, i.e., mu = mu(0) + mu(g), with the intrinsic friction coefficient mu(0) accounting for the chemical nature of the surfaces and the geometric friction coefficient mu(g) for the presence of nanotextures. We have found a possible correlation between mu(g) and the average local slope of the surface nanotextures.