FOLLOWING THE FASHION in such get-togethers, the White House Conference on Aging began yesterday in the midst of a blow-up over agenda, delegates and procedures. It would hardly be a White House Conference without the predictable tussling, but there are real issues here too.

Last year, through almost 200 separate programs, the elderly claimed about one-fourth of the federal budget. Next year, despite large cuts in most domestic spending, that share will rise to 30 percent, or more than $ 7,500 for each person over age 65.

By most measures, federal aid for the aged has been a great success. Twenty years ago, over a third of the elderly were poor. Now, thanks primarily to Social Security cash benefits, less than 15 percent are counted as poor, even when the value of medical, food and housing benefits is left out of the count. Generally rising living standards, more adequate government benefits and modern medical science have brought a longer and fuller life to most older people. The great majority of the aged own their own homes -- usually outright or with low-rate mortgages -- and most can afford to live independently. In recent years, moreover, indexing of Social Security benefits -- the major source of income for over 60 percent of the aged -- has provided better inflation protection for the old than most wage earners have had.

Inflation, however, has not been without its costs to the elderly. Few private pensions are adjusted for rising prices. The aged are also heavily represented among the depositors in savings and loan accounts and the holders of long-term bonds. They received negative returns, after adjusting for inflation, on their investments to the great benefit of those generally non-elderly people who bought cars and houses over the last decade. Losses of this kind are a special source of anxiety for the old who have little chance to recoup when the economy improves.

Overshadowing all these immediate difficulties, however, is the growing concern that the consensus that has supported vast increases in public spending for the old may begin to break down. The proportion of people who are old -- especially those who are very old -- will continue to grow over the next 30 years and accelerate sharply thereafter. You can quibble over the numbers somewhat, but it is an almost inescapable conclusion that, by the second quarter of the next century, maintaining the present structure of retirement and medical benefits will claim about a quarter of workers' earnings.

This wouldn't leave room for many other public benefits -- such as education and health care for children. It used to be that the interests of the old and young were frequently pitted against each other in families forced to choose between, say, an operation for mother and college for the kids. An expanding view of public responsibility has made those agonizing choices less frequent. It's worth some thought as to whether there are not some compromises to be made now -- perhaps in a gradual postponement of the retirement age or an expanded role for private pensions and savings -- that can avoid a replay of that inter-generational competition in the public policy choices faced by the next generation.