Cat joint bent backwards and vomit

a young cat, born in january, suddenly, today, wthout falling and without accidents, suddenly had trouble walking. His right front leg was bent backwards, and he wasnt placing the foot on the floor when walking, he was placing the joint itself. Then, 1 hour later, during which he vomitted his most recent food, the same thing started happening to the other front leg. What is happening?

Hello - and I'm afraid that I don't know, and that this sounds to be what is known as an 'interesting case.'  The knuckling sounds to be neurological in origin, perhaps linked to fitting (not all fits involve tonic-clonic seizures or falling) or a brain or spinal change. Your vet might do a neurological exam, to assess how well the nerves work, and to take it from there.  I don't know where abouts in the world you are, but there may be infectious diseases to take into account, for example tapeworms, toxoplasmosis or FIP.  Vets frequently start by identifying the main body system resposible for most of the symptoms, and then by considering possible causes of what they are seeing (the differentials list) and then doing tests to narrow it down.