We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient method to derive an upper bound to the maximum a posteriori probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP performance of regular LDPC codes improves with the alphabet size. We then consider nonbinary SC-LDPC codes, and show that, contrary to regular and irregular LDPC codes, the BP threshold of nonbinary SC-LDPC codes with large termination length improves with the number of bits per symbol and tends to the Shannon limit. We finally show that threshold saturation also occurs for nonbinary SC-LDPC codes.