In this Letter, we investigate, using molecular dynamics simulations, the diffusion of n-octane and n-tetradecane on a graphite surface at 300 K under incomplete coverage condition. For both molecules, we observe that the lateral diffusion coefficient exhibits a Lambda-shape anomaly with surface coverage i.e., the diffusion coefficient increases with the increase in surface coverage until a critical surface coverage, beyond which the diffusion coefficient decreases. Moreover, for low surface coverages, the longer n-tetradecane molecule moves faster compared to the shorter n-octane molecule and for high surface coverages, the n-octane molecule moves faster. We develop a new theory to understand the surface diffusion of n-alkanes and show that D similar to r(2)cc/N(P)t(R). (C) 2007 Elsevier B.V. All rights reserved.