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We analyze the delay performance of RTS/CTS-based (Request-To-Send/Clear-To-Send) multi-channel MAC (Medium Access Control) schemes for wireless networks. These schemes usually employ multiple data subchannels for data transmission and one control subchannel to send the RTS/CTS dialogue for channel reservation. Through theoretical analysis and simulations, we show that, in fully-connected networks, such multi-channel MAC schemes suffer longer delays than the corresponding single channel MAC scheme, that puts the RTS/CTS dialogue on the same channel as data packet transmissions. This conclusion holds even when data packets have different priorities and higher priority traffic is sent ahead of lower priority traffic.