Beagles have no recommended health tests and are generally fairly healthy. Apart from overeating hehe.
There are cases of Meningitis in young beagles which is currently being researched.
Beagles ARE a generally healthy breed if obtained from a competent breeder - not foolproof though. A good friend of mine had to have her Beagle put down at the age of 6 due to Amyloidosis. She had had a lifetime battle with food allergies with him as well. These conditions are listed as Beagle Health Concerns on a pet insurance site.
More Common Conditions:
- Cherry Eye
- CPRA-Central Progressive Retinal Atrophy
- Epilepsy
- Glaucoma
- Hip Dysplasia
- Intervertebral Disc Disease
- Patellar Luxation
Less Common Conditions:
- Amyloidosis (leads to organ disfunction)
- Cataract
- Deafness
- Demodicosis
- Distichiasis
- Hemophilia
- KCS-Keratoconjunctivitis Sicca
- Umbilical Hernia
https://www.trupanionpetinsurance.com/BreedGuide/Dog/Beagle
Pugs are also a much healthier breed than people make out. The only genetic problems then can be prone to getting are hemivertebrae and HD. Any other problems are bred in by people breeding poorly, or for exaggeration

They have no KC recommended health tests.
Just some additions here of conditions that can be a problem in Pugs. These are things breeders should be watching for and keeping record of in their breeding stock and relatives.
- On OFA the Pug dysplastic rate for HD is 68%
- Pug Dog Encephalitis is another genetic problem this breed is prone to.
- Dry Eye Syndrome or Keratoconjunctivitis Sicca (KCS) is a serious potentially blinding condition that Pugs suffer from.
- Legg-Calve-Perthes Disease (coxa plana or LCP Disease)
Portosystemic Shunt (PSS)
- Patella Luxation
- Brachycephalic Syndrome
- Elongated Soft Palate
- Entropion
- skin issues
- This is another breed in which breeders must watch for Syringomyelia as there are affected members.
- Stenotic Nares
- Cleft Palate
- Liver shunt
I find the pet insurance sites are often good to go to for the low down on potential health difficulties to watch for in breeds. This is a link I sometimes work from.
https://www.trupanionpetinsurance.com/BreedGuide/Dog-Breeds
CC