Friction measurements on muscovite mica and glass have been performed with a friction force microscope using Si3N4 tips. The environment was changed from ambient conditions to N2- or Ar-gas conditions. In ambient conditions, the friction-versus-load curves showed a nonlinear behavior closely following the Hertzian contact mechanics of a single-asperity contact: friction force ∼load2/3. For the same tip under gaseous conditions the friction force increased linearly with the load, indicating multi-asperity contact. A new model is proposed to explain this change in the nature of the friction behavior. In this composite-tip model, the tip is formed by the actual Si3N4 tip and ‘‘solidlike’’ contaminants present in enclosed cavities between tip and sample surface.