Severe Tropical Cyclone Glenda was among the strongest tropical cyclones to threaten Western Australia, though it weakened considerably before landfall and moved ashore in a lightly populated region. It began as a tropical low on 15 March in the Gulf of Carpentaria. The precursor disturbance drifted over Top End and later across the northeastern portion of Western Australia, and after emerging into the Indian Ocean it strengthened into a tropical storm. Aided by favourable environmental conditions, Glenda rapidly intensified to reach Category 5 status on the Australian cyclone scale, and with a peak intensity of 910 mbar it was among the strongest cyclones on record within the Australia region. On 30 March it moved ashore near Onslow as a Category 3 cyclone, and the next day it degenerated into a remnant tropical low over land.

Severe Tropical Cyclone Vance was a tropical cyclone that struck Western Australia during the active 1998–99 Australian region cyclone season, and was also one of six tropical cyclones to form off the coast of Australia during that season. When making landfall the Learmonth Meteorological Office recorded the highest Australian wind gust of 267 km/h (166 mph). The previous highest gust was 259 km/h (161 mph) at nearby Mardie during Cyclone Trixie. This record was surpassed in 2010 after a world record wind-gust of 408 km/h (254 mph) at Barrow Island during Cyclone Olivia in 1996 was declared official by the World Meteorological Organisation.