Following the lead of the airlines, Amtrak soon will begin offering special round-trip discount fares for long-distance trips this winter.

The National Railroad Passenger Corp. announced yesterday that beginning Jan. 10, Amtrak will sell some round-trip tickets for only $10 more than the one-way fare. This fare, which will be good for any trips up to April 1, will be available only for trips where one-way fares are at least $45.

The discounts will be available for most Amtrak trains in the East, including Florida trains.

However, trips within the Washington-Boston Northeast corridor won't be eligible for the discounts.

In many cases, the new fare will be substantially lower than the round-trip excursion rate Amtrak now offers. For example, under the new fare, a round trip between New York and Miami will be $151 compared with the $179 excursion fare.

The special fare for a Chicago-New Orleans trip will be $113, which is $52 less than the excursion fare. The fare between Chicago and New York will be $117, compared with a $172 excursion fare.

The discount will be available for only a limited number of seats on each train. But Amtrak noted that most customers should be able to qualify for the bargains.