We study the coverage dependence of surface diffusion for chainlike molecules by the fluctuating-bond model with a Monte Carlo dynamics. The model includes short-ranged excluded volume interactions between different chains as well as an intrachain bond angle potential to describe the chain stiffness. Our primary aim is to consider the role played by chain stiffness and the resulting memory effects in tracer diffusion, and in particular their role in the effective tracer diffusion barrier E-A(T) extracted from the well-known Arrhenius form. We show that the memory effects in tracer diffusion become more pronounced at an increasing coverage as a result of packing requirements. Increasing the chain flexibility furthermore has the same overall effect as increasing the chain length, namely, they both increase E-A(T). We then analyze the influence of memory effects on E-A(T) and find that, for a single diffusing chain, about 20% of E-A(T) arises from temperature variations in the memory effects, while only the remaining part comes from thermally activated chain segment movements. At a finite coverage, the memory contribution in E-A(T) is even larger and is typically about 20%-40%. Further studies with chains of different lengths lead to a conclusion that, for a single diffusing chain, the memory contribution in E-A(T) decreases along with an increasing chain length and is almost negligible in the case of very long chains. Finally, we close this work by discussing our results in light of recent experimental work as regards surface diffusion of long DNA molecules on a biological interface. (C) 2000 American Institute of Physics. [S0021-9606(00)70110-3].