As the name suggests, consecutive cruises are scheduled back-to-back, with the traveler leaving one cruise ship to embark on another cruise ship with a new travel itinerary. According to the law in the U.S., you cannot take consecutive cruises where the first itinerary begins at one U.S. port and the second trip itinerary ends in a different U.S. port. If Azamara finds that a consecutive cruise has violated this rule, it has the right to cancel the sailing and issue a refund.