Banking institutions are starting to fight the money-market mutual funds on their own turf. They're finding ways to compete aggressively for your savings dollar by offering high interest rates and ready access to your money.

New-breed accounts, at many banks, savings and loans and some credit unions, are well worth the attention of anyone who hasn't switched to money funds, or who finds his or her money fund inconvenient.

So far, only the more aggressive institutions offer money-fund look-alikes. And even where offered, they do pose some slight credit risks, as explained below.

But as time passes and banking regulations change, these accounts should grow more attractive and spread to all the best and brightest institutions. Some of the $202 billion now held by money-market mutual funds will start leaking back to the corner bank or S&L.

The major banking institutions still operate under a handicap. Federal laws depress the interest rates available on passbook savings accounts, and require high minimum deposits on short-term savings certificates.

But deregulation is proceeding through the back door. Within a short period of time, any bank or S&L that can afford it should be free to offer uninsured money-fund look-alikes. At federal credit unions, which account for 4.9 percent of the nation's savings, interest-rate limits on all types of accounts were abolished entirely on April 21.

What's already on the market, or coming your way:

1. Savings and loan associations recently won permission from the government to offer you an automatically renewable retail repurchase investment. From the point of view of a depositor, a renewable "repo" acts very much like a money fund. It's an uninsured investment, paying high current interest rates that can change as often as every day. Money can be withdrawn at any time without penalty. Some S&Ls even advertise these accounts as "money funds."

They are not funds. Your money is not invested in a diversified portfolio of short-term securities, as it would be in a real money fund. A retail repo, by any name, is a straight loan to your S&L, guaranteed by the S&L's own solvency. Repos are generally "backed" by federal securities, but on a daily basis the market value of the securities isn't always exactly the same as your investment. If the S&L went broke, you could lose a little money. This risk is small, but it's there.

Banks have requested, and should receive, similar authority to offer automatically renewable repos. Minimum deposits range from $2,000 to $5,000, depending on the institution. You cannot write checks against a repo, but these accounts are generally linked with insured 5 1/4 percent interest-paying checking accounts.

One warning: Many of the interest-rate comparisons you see in ads today are highly misleading. Banks, S&Ls and money funds may all pay compound interest on your savings. But under the law, money funds cannot show the effect of interest compounding in their advertisements, while banks and S&Ls can. With monthly compounding, a money fund at 14 percent may be paying you exactly the same dollar return as an S&L repo advertising 14.9 percent. Yet the S&L may claim that it's paying more. The laws should be changed to stop these phony sales tactics.

2. An increasing number of credit unions pay high interest rates on deposits over $1,000 or $2,000, some of them going as high as 11 or 12 percent. A few credit unions have their own brand of money fund, although most lack the sophistication to handle such a complicated account.

3. In Maryland, Ohio and North Carolina, some S&Ls carry private deposit insurance. This frees them from federal interest-rate limits, and lets them offer insured, high-interest money-fund look-alikes.

For safety-conscious savers, the question is: Who insures these accounts? In Maryland, it's the Maryland Savings-Share Insurance Corp., supported by 105 participating institutions and in good financial health. Private insurance is subject to state regulation. But there is no state or federal guarantee. You are counting on the S&Ls, or other private insurers, to remain strong enough to meet their commitments. It's a good bet--but something to weigh if perfect safety is your main concern.