Here's Why People In NJ Can't Own Axolotls Photo by T K on Unsplash loading...Why Are Axolotls Illegal In New Jersey? The main reason axolotls are on NJ's illegal pet list is due to a little thing called "hybrid vigor." While it sounds cool, it's a huge problem for native species. Axolotls Illegal To Own in NJ Photo by Mattias Banguese on Unsplash loading... The Real Threat Of HybridizationWhen a hybrid species is more competitive than the native species, it can quickly outcompete them for food, territory, and other resources.