If you are traveling with your pet across the borders, you may need to possess a pet passport as identity of your pet. For cats and dogs, passports are specified for each country, each country has their own laws. You must have knowledge about the requirements of the country of destination where you are traveling to. Knowing the import rules will make it easy to travel.
PETS, the Pets Travel Scheme defines the traveling laws allowing animals travel in member countries without undergoing quarantine. A passport for pets lays information about the pet, its owner, country of owner and other necessary information.
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Some of countries accept only formal passport otherwise a normal paper containing above information is sufficient. Additionally rabies vaccination certificate (Especially in Europe) showing that pet was vaccinated within three weeks, must be endorsed. Some countries like UK and Japan ask for tapeworm treated certificate and other countries ask having a fitness certificate. Some countries like Japan authorities ask that pet must have a microchip in the skin.