From GoToCayman.com - the Wiki for Cayman
In addition to personal effects for use while on vacation, visitors over 18 are allowed a duty-free allowance of one litre of alcohol or four litres of wine or one case of beer (not exceeding eight litres) and 200 cigarettes, or 50 cigars or 250 grams of tobacco. This limit should not be confused with the Customs forms which state that returning residents are allowed CI$300 worth of goods duty free. This privilege does not apply to visitors. There are a number of liquor stores on the islands, but the licensing laws are very strict; they have to shut by 7pm on Mondays to Saturdays and are closed on Sundays.