You can use this problem as an opportunity to build trust with your child. This is your time to shine in many roles, such as protector and teacher. Empathize and acknowledge your child's fears, yet don't reinforce them. Here are some easy ways to very gradually introduce your child to the concept of pets:

Take a trip to the toy store. Browse around the fuzzy stuffed animal section. Start petting a bunch of them yourself and let your child copy. Let him pick out his favorite stuffed animal dog or cat. This introduces him to the concept of "dog" and "cat" in a fearless way.

Read fun animal books. Pick out ones in which the animals are playful and joyful and not scary. Read the books to him while you ask him questions, such as: "Where's the nice dog?" or, "Where's the pretty cat?" All the while, you're planting in his mind that these animals are fun, safe, and not scary. Avoid TV and stories that have scary animals in them. These will only set him back and are likely to trigger scary nightmares where he sees the dogs and cats as monsters in his room.

Try a trip to the pet store. After a while, browse a pet shop where he can see cute little kittens and puppies. When your son seems ready, encourage him to hold and pet the puppies and kittens. If he's still fearful, take advantage of your parent-child trust. Just sit and pet the animals awhile, hoping your child will copy. If he sees that you are not afraid of dogs and cats -- and even enjoy them -- he will eventually feel likewise.

Try peer pressure. Visit with friends who have toddlers and pets. Let your child see how children his age play and have fun with their pets. Realize that as you help your child overcome the fear of dogs and cats, you're probably setting yourself up to bring home a puppy or kitten -- or both.