Anxiety is not a problem exclusive to humans. Many pets have anxiety about separation from their owner, aggressive pets with whom they share their home, and other issues. The medications used to help animals with these issues are the same medications that humans use. Clomipramine is the first to achieve FDA approval for use in dogs as well as humans.
There are many uses for this medication since it is effective as an anti-anxiety medication, a muscle relaxant, an appetite stimulant, and a seizure control drug. The injectable form of diazepam is often used in anesthetic protocols.
In dogs and cats, phenobarbital is probably the first choice for seizure suppression. It is effective, safe if used responsibly, and is one of the least expensive medications in all of veterinary practice.