You wouldn't normally think that eggplant and peppers would need the kind of support you'd give tomatoes. In fact, if you get the sort of yields you see in seed-catalogue photographs, you're more than likely to find branches broken by the weight of the fruit.

A year or two ago, the PBS show "Victory Garden" demonstrated the cultivation of eggplants as vines. In a gigantic greenhouse in England the plants were trained up wires that rose 10 to 20 feet and, as I recall, were trimmed of all but a central stalk. The shiny purple fruit hanging from these "vines" were impressive indeed.

While I haven't gone that far in eggplant- cultivating, I did give my eggplants support last year for the first time after years of watching branches split apart and fruit discoloring on the ground. I was rewarded by a harvest that doubled previous yields.

I kept meaning to do the same for the peppers and never got around to it. As plants grew and fruited, they, too, often split and I lost some peppers to ground rot. While the splitting of the branches doesn't seem to have a serious effect on production, it's unattractive and makes harvesting tricky because you can accidentally break off a whole branch when picking the fruit.

Eggplants don't need elaborate support. I use inch-square stakes of the sort you buy for tomatoes. I prefer construction-wire cages for tomatoes, but the stakes are very useful for eggplants, peppers and dahlias. Or you can use commercially available tomato cages, lightweight four-sided contraptions that I think are also inadequate for tomatoes.

If you stake the plants, pick up a couple of rolls of green plastic rose tape. It's very pliable and won't dig into the plant's stem where you tie it to the stake. Just keep an eye on the plant as it grows and tie it up when it gets taller. Now's the time to put your stakes in, before root systems have gotten so large that they're likely to be damaged by the jamming down of a stake. If you give your plants support for a year, you may well find, as I did, that you can reduce the number of plants because your yield increases so much.

Another advantage of giving your vegetable plants some vertical support is that it can save quite a bit of space, as well as benefit the plant. Take melons and cucumbers. You can grow them on the ground and let them wander about, consuming valuable soil areas. It certainly is the easy way, and is commendable for that reason alone. But if you go one step further and erect a sturdy fence of some sort, the melon and cuke vines will go right up the fence with minimal encouragement, and the fruit will be much easier to locate and pick.

One disadvantage is that most melons and even some winter squashes -- spaghetti squash and other large varieties -- will need additional support later. The fruit itself should be encased in a sling so that its weight won't cause it to break off the vine before it's fully ripe. This can be too much of a hassle for many gardeners, but if you have a little extra time, it's worth doing in terms of the extra harvest and the saved space in the garden. If you're skeptical, just try one this year, and see if you don't note a difference.

One word of caution on training cukes and other vining summer squashes. If you must force them onto your fence support, do so with great care. Handling and possible ensuing injury can leave the vines extremely susceptible to cucumber wilt. Rather than risk that, I suggest you leave the plants alone until they've grown large enough to climb the support by themselves. They'll figure it out if you give them a chance.

And finally, don't use chicken wire to support vining crops in the garden. When the harvest is over and it comes time to remove the vines, the small weave of chicken wire makes the process difficult. Often vines are overly tangled, and getting them out of the little openings is very time- consuming. Too, chicken wire by itself isn't sturdy enough -- you need to frame it, which means putting out more money. Use snowfence, American woven wire or even a post-and-board combination. The fence can be permanent -- just rotate what you grow on which portion of the fence each year and add organic matter to the soil a couple of times a year.

LIVING LEGENDS -- The National Arboretum, in conjunction with its Living Legends from Around the World program, is sponsoring a class -- Roses: Heirlooms that Flower and Fruit -- Sunday at 1:30. In cooperation with the British embassy there'll be a special showing of the Queen Elizabeth Rose. At 3, horticulturalists will hold a question-and-answer session. Members of the National Capital Area Federation of Garden Clubs, Inc. will serve up samples of food from Great Britain at 3. The Arboretum is at 3501 New York Avenue NE. There's plenty of free parking. If you plan to attend call 475-4815. The lecture is in the Administration Building's auditorium..