The wireless local area network (WLAN) and wireless ATM are emerging technologies for wideband wireless local access. Two standards, IEEE 802.11 and ETSI HIPERLAN type 1, are currently available for WLAN; the standardization process of wireless ATM, involving, among others, the wireless ATM Group of the ATM Forum and the broadband radio access networks project of the ETSI, is ongoing and related standards are expected to be released by mid-1999. This article focuses on the MAC protocol aspects of wireless local access networks. It first investigates, from a traffic performance point of view, the MAC protocol of the IEEE 802.11 and ETSI HIPERLAN type 1 standards, and then verifies to what extent these MAC protocols are suitable for wireless ATM. The analysis is then extended by considering a new MAC protocol, dynamic slot assignment (DSA++), which has been designed to explicitly support ATM technology over the radio interface. DSA++ is a candidate for the ETSI HIPERLAN type 2 standard, a developing ETSI standard for wireless ATM.