Compensation for a Type A free agent is a first-round pick (unless it is lower than 15th overall) and a sandwich selection between the first and second rounds.
For lost Type B free agents, teams will receive a sandwich pick after the first round.
Even though the Marlins didn't offer arbitration to their free agents, they still can continue negotiating with the players.
Rhodes, 39, enjoyed a strong 2008 season. The left-hander was acquired July 31 from Seattle for pitching prospect Gaby Hernandez.
Used as a situational lefty, Rhodes appeared in 25 games for Florida, and he was 2-0 with an 0.68 ERA. He allowed just one earned run in 13 1/3 innings, striking out 14 and walking three. Opponents had 11 hits off him.
While with the Mariners, he was 2-1 with a 2.86 ERA, giving up seven earned runs in 22 innings.
The veteran, who has playoff experience from his days with the Orioles and Mariners, already is drawing heavy interest from other clubs.
Rhodes broke in with Baltimore in 1991, and he has appeared in 653 Major League games.
Gonzalez, 41, offered veteran leadership on a youthful squad this past season. He started in right field on Opening Day because Jeremy Hermida was on the disabled list. It was the 18th straight season Gonzalez has started in the big leagues.
The left-handed hitting outfielder is hopeful of playing at least one more season. There still are some milestones he would like to reach. Gonzalez has 596 career doubles, and the No. 600 is important to him. He also has 2,591 hits and 354 home runs.
In all likelihood, Gonzalez will sign with another club. He is even considering joining an American League squad with which he could be used as a designated hitter.
Lo Duca, 36, played in 21 games with the Marlins after he signed a Minor League deal on Aug. 9. The veteran batted .294 in 34 at-bats as John Baker's backup.
Hendrickson, the Opening Day starter in 2008, made 19 starts for the Marlins in the first half. But he was switched to the bullpen in July, and he mostly was used in long relief.