Every day, the estimated 42 percent of American households that own at least one pet are literally deluged with "expert advice" on everything from what to feed their animals to how to train them to do tricks. But one area in which advice has been lacking is the one experience every pet owner will sooner or later have to face -- that pet's death.

One person working to change that situation is Jamie Quackenbush, the nation's first full-time pet bereavement counselor. Quackenbush estimates that he helped about 1,000 people deal with the death of their pets last year in his job at the University of Pennsylvania Veterinary School's Center for the Interaction of Animals and Society.

"Most everybody doesn't understand what's involved in the loss process," says Quackenbush, who was trained as a social worker and came to his job at Penn "kind of by mistake" in 1979, when he was looking for financial assistance while he pursued his doctorate.

Nevertheless, with the medical community's growing recognition of the important role of pets, pet bereavement is becoming, if not fashionable, at least accepted.

"It's not like all of a sudden people are feeling a greater attachment toward their animals," says Quackenbush. "We've been grieving over lost pets ever since humans began owning animals. It's just that, in a sense, it's come out of the closet for many people. For many, many years it was literally a closet experience, and everybody kind of stuffed it away and suffered."

Although most people would hesitate to put the pain of losing a cherished pet into the same category as losing a human family member, Quackenbush insists that differences are minimal.

"For all practical purposes, the loss sequence that people go through emotionally and psychologically when a pet dies is virtually indistinguishable from the one that we would go through if a human dies. We as human beings only have one fundamental way of dealing with loss, and it's always going to be the same."

The death of a pet may be doubly difficult because people are unprepared for the depth of their reactions. "We pretty much know that if a special person in our life dies, we're going to be a mess," says Quackenbush, who with free-lance writer Denise Graveline has written a book, When Your Pet Dies: How to Cope With Your Feelings (Simon and Schuster, $15.95).

"If a child or a spouse or a parent dies, we know that it's really going to shake our emotional foundations. And while we care a lot about our pets, until one experiences that loss, many people never anticipate the depth and the intensity of their feelings."

The other key factor most people fail to grasp about bereavement, says Quackenbush, is that it's a process.

"There's a beginning point, a middle point and then eventually an end point. And by and large, throughout this process we feel bad . . . It's the way that we come to accept and live with the deaths that we experience. It's a painful process, but getting better, is, in effect, feeling bad."

That doesn't mean, of course, that the healing process can't be made easier, and that's where Quackenbush comes in. With the help of a graduate student who comes in two days a week, Quackenbush operates in what he calls a "crisis-intervention mode." Often his services are sought not only when an animal has died, but when owners are faced with having to make life-or-death decisions for their pets.

* While individuals vary in their reactions to the death of a pet, it may have little to do, says Quackenbush, with whether it was a cat or a dog or even a goldfish. "It can literally be any living thing," he says, recounting the tale of one of his patients, a little old man whose three pet white rats died suddenly of an unexplained illness. "He was really heartbroken. It was a very, very difficult experience for him."

Although he says he doesn't like to generalize, Quackenbush concedes that the grief process generally includes periods of denial, anger, bargaining, depression and, finally, acceptance. "I avoid saying that there are five stages simply because it is almost always interpreted so literally. When people see that or hear that, then the first thing they will automatically assume is that if they don't do that there's something wrong with them."

While it's rare that the death of a pet itself causes a serious emotional health problem, people with histories of emotional problems or depression are at risk. With those people, says Quackenbush, "You can just about bet that first, they've gotten very close to their animals, and second, that death is going to be, in a sense, kind of like the proverbial straw."

Signs that a person needs professional help, he says, include a serious or prolonged depression or a general inability to function.

One thing Quackenbush is careful not to recommend is that grieving owners rush right out and get a new pet. "In most cases, when you introduce a new animal in there, that can very effectively impede the whole grieving process. One of the things people seem to want to be very sure of is that they aren't going to forget Spot, and when Spot dies and you feel rotten and you go down and buy a new puppy, then it's a very strong suggestion that our pets aren't a whole lot different from our toasters. And that couldn't be further from the truth."

It's best, says Quackenbush, for owners to wait until they've become accustomed to a new life style without the pet, and then to introduce a new animal -- preferably a different kind -- on its own terms.

First, the animal isn't going to be just like the other one because dogs and cats are as different from each other as people are, and second, you'll always be reminding yourself of the one that's gone."