Unlike single-C(60)-based devices, molecular assemblies based on two or more appropriately connected C(60) molecules have the potential to exhibit negative differential resistance (NDR). In this work, we evaluate electron transport properties of molecular devices built from two C(60) molecules connected by an alkane chain, using a nonequilibrium Green function technique implemented within the framework of density functional theory. We find that electronic conduction in these systems is mediated by the lowest unoccupied molecular orbitals (LUMOs) of C(60), as in the case of a single-C(60)-based device. However, as the positions of the LUMOs are pinned to the chemical potentials of their respective electrodes, their relative alignment shifts with applied bias and leads to a NDR at a very low bias. Furthermore, the position and magnitude of the NDR can be tuned by chemical modification of the C(60) molecules. The role of the attached molecules is to shift the LUMO position and break the symmetry between the forward and reverse currents. The NDR feature can also be controlled by changing the length of the alkane linker. The flexibility and richness of C(60)-based molecular electronics components point to a potentially promising route for the design of molecular devices and chemical sensors.