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Abstract: Hyperentanglement, defined as the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention recently. Here we investigate the possibility to concentrate the two-photon four-qubit systems in partially hyperentangled states in both the spatial-mode and the polarization DOFs with linear optics. We first introduce the parameter-splitting method to concentrate the systems in the partially hyperentangled states with known parameters, including partially hyperentangled Bell states and cluster states. Subsequently, we present another two nonlocal hyperentanglement concentration protocols (hyper-ECPs) for the systems in partially hyperentangled unknown states, resorting to the Schmidt projection method. It will be shown that the parameter-splitting method is very efficient and practical for the concentration of the quantum systems in partially entangled states with known parameters, resorting to linear-optical elements only. All these four hyper-ECPs may be useful in long-distance quantum communication based on hyperentanglement.