The credit union has grown into a full-time financial-service institution

Say ''credit union,'' and many people still get a mental picture of a little office where two or three staff members process payroll-deduction deposits and issue low-interest, easy-term loans. At some credit unions this is still the case, and those offices are staffed by people who have no professional training in banking, savings, or lending.

At more credit unions, however, that is no longer the case. The credit union is becoming a sophisticated place to do many of the things that can be done at banks, savings-and-loans, and money market funds. Credit unions, many of which are staffed by full-time professionals and backed by a nationwide credit union ''bank,'' can mostly match these institutions' claims of high interest rates, safety, and check writing privileges.

As a result, credit unions are as flexible and competitive a place for savings as most banks or savings-and-loans. And with the payroll deduction plans available at most company credit unions, it is easy to get on an automatic savings program that sets aside money for savings first, before you have a chance to spend the money on something else.

Unlike ordinary banks or money funds, however, not everyone is eligible to join a credit union. On the other hand, there are probably many who are eligible but don't know it. In addition to a company or union local credit union, there may be a town or county that is open to residents, or a credit union at one company may have expanded to accept employees from other companies in the area.

Some 50 million people do know they are eligible and have deposited over $80 billion in savings. That is less than half the deposits of the money funds, but almost all credit union deposits are from individuals, while about half of the money funds' deposits are from institutions and corporations.

To help attract more individuals, the Credit Union National Association (CUNA), the credit union trade association has been promoting the US Central Credit Union. CUNA calls US Central the only nationwide banking system in the country.

US Central consists of 42 ''corporate'' (state or regional) credit union organizations that provide financial services like local check clearing for some 20,000 individual credit unions in the country. US Central gives these credit unions professional guidance, extra liquidity, and correspondent banking services.

For a decade after it started in 1970, US Central remained fairly small. But after 1980 its assets jumped from $2 billion to about $8 billion, pushed by higher savings, fewer credit union loans when interest rates were high, and the addition of several new services that made US Central more attractive to local credit unions and their members.

Thanks to US Central, credit unions can offer their members money market funds invested in US government-backed securities, discount brokerage accounts, and individual retirement accounts.

The credit unions are also competing with money funds and banks directly by offering competitive rates on their ''share draft,'' or checking accounts. At many credit unions, these rates are equal to the money funds or the banks' money market deposit accounts. In some cases, they may even be better, because of the credit unions' lower expenses and account fees.