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: Can I get live assistance with a quote or purchase? Are there medical conditions that are not covered by travel insurance? Should I consider extending my return date to accomodate any unforseen delays in my return home? What other coverage is typically included in an AIG Travel Guard travel insurance plan? What is covered under the "Cancel for Work Reasons" benefit?