At about 21:20 Hawaiian standard time, a cargo-filled Boeing DC-10-30F sustained substantial damage to both elevators after responding to a TCAS alert five minutes after departure. No one was injured. The captain said the airplane departed runway 08R and he was turning right to a heading of 155 degrees and passing through 1,500 feet when air traffic control instructed him to turn left to 140 degrees for traffic. The traffic was at 10 oclock at 5,000 feet. The captain acknowledged the traffic in sight. The first officer advised the captain to shallow the climb to maintain separation. The other airplane, a Hawaiian Air DC-9, appeared to still be descending at 10 oclock. The TCAS in the DC-10 alerted for traffic and issued an advisory to climb at 1,200 fpm. The airplane was climbing through 3,800 feet as the captain pitched up to attain 1,200 to 1,500 feet per minute rate of climb. The TCAS then reported clear of conflict. The captain then contacted departure control to discuss the close encounter, but he did not file a near midair collision report. Departure control informed him they did not know if the DC-9 received a TCAS alert. The Hawaiian Air crew also received a TCAS alert when they were descending through 4,500 feet. The DC-10 proceeded to Fiji for a fuel stop and scheduled crew change. Both crews inspected the airplane and observed damage to both elevators. An Australian airworthiness inspector said the outboard lower skins of the elevators were severely bent, the horizontal stabilizer fairings were indented from contact with the elevator balance weights and many rivets were pulled through the upper skin.