Americans took on $5.1 billion more in consumer debt than they paid off in December, up slightly from the November increase but well below the torrid debt growth in earlier months, the government reported yesterday.

The Federal Reserve Board said the December credit increase compared with a $4.8 billion rise in November. Both months were far below the record $11.5 billion debt gain in September, which included heavy borrowing to finance new-car purchases. Debt grew in December at an annual rate of 11.5 percent, down from a rise at an annual rate of almost 20 percent during the past 12 months.

Some economists have predicted that consumers are likely to cut back sharply on purchases of big-ticket items such as cars and appliances in coming months because of heavy debt burdens.

The report showed debt growth in December was concentrated in the category that includes cash loans from banks and other short-term personal debt, which rose by $2.08 billion in December, up sharply from a $1.06 billion November increase. Credit-card debt rose by $1.3 billion in December, down from the November increase of $2.6 billion after adjusting for seasonal variations. The changes put total consumer debt outstanding at $541.37 billion at the end of December.