The Alexandria, Dukes, last season's orphans who have been adopted by the Pittsburgh Pirates' farm system and given virtually a new roster of players, begin their fourth season Friday against the Kinston Eagles in North Carolina. They open at home, also against Kinston, April 17 at Four Mile Run Park in Alexandria.

Last year, as a cooperative baseball club, the Dukes had players signed by seven major league organizations, but the team was not assembled, or a manager named until just before the season began. Alexandria finished last in its division of the Carolina League for both the first and second halves of the season.

"Things are looking much better this year," said Mike Toomey, the former baseball coach at George Washington University who became the Dukes' manager.

"We've had some nagging injuries, but we've also had some good practices and some good games. Last year we never had a chance to practice before our first game."

Since early last month, Toomey has been at the Pirates' baseball complex in Bradenton, Fla., where the Pirates, their Class AAA team from Portland, Ore., their AA team from Buffalo, N.Y., and their class A clubs, the Dukes and a team from Greenwood, S.C., go for spring training.

"We won't know for sure until the very last minute who will be on our club, probably not until we break camp," said Toomey, who also spent two months last fall in Florida at a Pirates organization school for managers.

Just after the season ended last year, the Pirates and the Dukes signed a three-year agreement of affiliation. Under the terms of that pact, the Pirates sign all the players and pay their salaries, in most cases between $600 and $2,000 a month. Meals and travel expenses are shared by the two organizations.

"This gives us so much more credibility and so much more stability," said General Manager Rick Holt. "It's good to be associated with the 1979 world champions, a team that is a perennial contender. It's good to be associated with a team from the East Coast."

Teams in the Carolina League. which includes a team from Hagerstown, Md., this year for the first time, play a 140-game schedule, with the season divided into halves. If different teams win the first and second halves in either of the two divisions, a one-game playoff will be held Aug. 31 to determine the division winners. Division winners will play a best-three-of-five series for the league title.

Organized in 1978 by Alexandria builder Eugene Thomas and a group of associates, the Dukes were not affiliated with any major league organization that year.

Their second season they were affiliated with the Seattle Mariners, but that relationship ended when the Mariners opted for a West Coast team as their Class A affiliate and the Dukes declined the Mariners' suggestions that they upgrade their program to AA.

The Dukes are to break camp Tuesday and will arrive here that night on a charter flight from Florida. Wednesday they will play an exhibition game with George Mason University at 7:30 p.m. at Four Mile Run Park, 3600 Commonwealth Ave., with proceeds from that contest going to George Mason's scholarship fund.

Weekday home games all will start at 7:30 p.m. Sunday home games begin at 2 p.m.