May I purchase a travel insurance policy with 'secondary' medical cover if I have no other medical insurance? Published by Chris Harvey February 20, 2009 Yes. Most all travel insurance plans with secondary coverage become primary in the event an insured has no other insurance. Related articles: One of the members of our family is much older than the rest of us. Does that effect the premium? What does "baggage delay" cover? What is "International Medical" travel insurance? My travel insurance policy excludes hazardous sports? What is considered a hazardous sport? I have already departed from my primary place of residence. May I purchase cancellation insurance for a return trip home?