When you stamp an envelope and mail the monthly check to your insurance company in Hartford, the check may take a circuitous route before it returns to your bank and is mailed back, canceled, in your monthly statement.

Probably no two banks process the check in exactly the same way, but bankers say the following scenario is as likely as any:

Several days after you mail it, the check is deposited by the insurance company at its bank in Hartford. The bank credits the insurance company's account conditionally (in case the check bounces) and encodes the amount and a routing number on the lower right hand corner of the check so special mechanical devices can read it along its journey back to your bank.

Then the Hartford bank sorts the check, probably one of thousands that were deposited that day. In this case, because the check likely is a small one, the Hartford bank bundles it up with other checks bound for Washington and sends it to the nearest Federal Reserve Bank, in Boston.

The Hartford bank maintains what is called a reserve account with the Boston Federal Reserve. The Boston Federal Reserve credits the bank for the amount of your check, again conditionally, and ships the check to the Baltimore branch of the Richmond Federal Reserve Bank.

Your Washington bank maintains an account with the Baltimore branch of the Fed. The Fed debits the Washington bank's account for the amount of your check, then ships the check to your bank. Your bank then debits your account for the amount of the check and files it.

If your account did not have sufficient funds to cover the check, your bank might well "bounce" it, that is stamp it "insufficient funds" and send it back to the Baltimore Fed. The check will retrace its route back to the Hartford bank.

Many checks, however, are written on banks in the same area in which they are deposited. Banks have developed local clearing houses, where couriers meet each morning to exchange checks. Riggs National Bank, for example, might have 2,000 checks written on American Security for a total of $2 million, while American Security might have 2,300 Riggs checks totaling $1.9 million. American Security would owe Riggs a net of $100,000. American Security could either pay Riggs directly, or call the Fed and have $100,000 transferred from its account there to the Riggs account.

In some cases, a bank or banks in one part of the country may have many checks written on banks in another part of the country. A big Chicago bank, which is also the correspondent for dozens or hundreds of other Chicago-area banks, might present its checks directly to, say, Citibank in New York rather than going through the Federal Reserve system.

About 16 billion of the 40 billion checks written each year are cleared through the Fed and the rest are processed through local clearing houses or bypass the Fed some other way.