Authorities urged residents to be on alert as Tropical Storm Wilma's outer edge neared the Cayman Islands, packing strong rain and wind as it cut a path that could threaten Cuba and Florida. Wilma became the Atlantic hurricane season's 21st named storm before dawn Monday, tying the record set in 1933 and exhausting the list of storm names. It could strengthen into the year's 12th hurricane by Tuesday. That many hurricanes formed in 1969, the most since record keeping began in 1851. Forecasters said Wilma could grow into a minimal Category 1 hurricane by Tuesday afternoon. Computer models initially showed Wilma heading for Mexico's Yucatan Peninsula by Friday, but the forecast track based on the models shifted east by 11 p.m. E.D.T. Monday, placing the storm closer to western Cuba than the Yucatan on Friday. The storm was forecast to then turn sharply in the Gulf of Mexico toward Florida over the weekend. Conditions such as warm water and favorable atmospheric winds are in place for Wilma to strengthen, possibly into a major hurricane with winds above 177 kph. "If it goes through the Yucatan Channel, there won't be much to weaken it," Mayfield said.