Molecular communication is a new nano-scale communication paradigm that enables nanomachines to communicate with each other by emitting molecules to their surrounding environment. Nanonetworks are also envisioned to be composed of a number of nanomachines with molecular communication capability that are deployed in an environment to share specific molecular information such as odor, flavour, light, or any chemical state. In this paper, using the principles of natural ligand-receptor binding mechanisms in biology, we first derive a capacity expression for single molecular channel in which a single Transmitter Nanomachine (TN) communicates with a single Receiver Nanomachine (RN). Then, we investigate the capacity of the molecular multiple-access channel in which multiple TNs communicate with a single RN. Numerical results reveal that high molecular communication capacities can be attainable for the single and multiple-access molecular channels.