McHugh asked for a raise from $3.85 million to $5 million during Tuesday's hearing before arbitrators Mark Burstein, Jeanne Wood and Allen Ponak. Houston argued for a $4.55 million salary.
Garcia requested a hike from $3 million to $6.7 million rather than Chicago's $5.85 million offer. His case was heard by Phillip LaPorte, Steven Wolf and John Kagel, who are likely to issue a decision Wednesday.
Players lead 7-6 with decisions to be announced Thursday for McHugh and pitchers Marcus Stroman, Jake Odorizzi and Trevor Bauer. Four more hearings are scheduled, and 22 decisions would be the most since players won 14 of 24 cases in 1990.
McHugh heads to spring training projected as a sixth starter behind a rotation of Justin Verlander, Dallas Keuchel, Gerrit Cole, Lance McCullers Jr. and Charlie Morton. The Astros could decide to trade McHugh.
The 30-year-old right-hander was 5-2 with a 3.55 ERA in 12 starts last season. He was on the disabled list with tendinitis in his pitching shoulder until July 22.
Astros closer Ken Giles won his case on Feb. 3 and will earn $4.6 million instead of the team's $4.2 million offer.
Garcia was a first-time All-Star last year, when he was second in the AL batting race and set career bests with a .330 average, 18 homers and 80 RBIs.
Information from The Associated Press was used in this report.