Sue Ellen returns to Southfork and neglects returning to Dallas to visit her son, much to the chagrin of the rest of the family. Bobby takes it upon himself to run interference for JR when Cliff continues poking around the hospital. On the ranch, a virus begins taking livestock and concerns Jock and Ray.
The family gathers itself at Southfork after the baby is kidnapped. Bobby goes after Cliff, thinking he's taken JR's son, while Jock is sent on a wild goose chase. JR, meanwhile, gets a call from some old friends who claim to have something to do with the kidnapping.
Digger Barnes returns to Dallas and collapses in Cliff's apartment which is followed by a visit to the hospital and it's revealed that Digger carries a neurological disease that turns out to be hereditary. Although Cliff and Pam are fine, any children that they may bear have a lower-than-normal mortality rate, which puts Pam's marriage to Bobby in jeopardy and Cliff wonders about his son... John Ross Ewing III.
Valene returns and tries to win a resistant Lucy's understanding. Pam discovers she is pregnant and struggles with how to tell Bobby about both the baby and her own recently discovered genetic disease.
Kristin convince J.R. to give her a summer job at Ewing Oil and begins flirting with him in earnest. Bobby learns Pam is pregnant, but not about her genetic disease. J.R. makes a business deal that may put Southfork at risk.
Jock, Bobby, J.R. and Ray take time off to go on a hunting trip. Once there they encounter a farmer who Jock strong armed 40 years ago and who is seeking revenge. Afraid he might not make it out of the encounter Jock confides a secret to J.R. and asks him to do something that might bring J.R.'s recent shady dealings to light. Back at the ranch Miss Ellie takes advantage of the men's absence to make a worrying doctor's appointment.
Bobby becomes close to the son of one of the ranch hands. Pam tries to find a way to tell Bobby about the risk to their unborn child. J.R. becomes suspicious of Sue Ellen and hires a detective to follow her.
The Ewings host a rodeo. J.R. uses the event as an excuse to further his plans to destroy Cliff and openly flirt with Kristin. Digger uses it as an opportunity to see John Ross III, who he believes to be his grandson. Sue Ellen flirts with cowboy Dusty Farlow.
Ellie deals with the aftermath of her mastectomy and her anger at Jock keeping something from her for 40 years. Digger tell Miss Ellie he still loves her. Lucy fears she will inherit breast cancer. Jock and Bobby find out about J.R.'s plan to displace Cliff. Dusty tries to convince Sue Ellen to leave J.R.
Lucy throws herself at Alan Beam, who sees her as a ticket to the good life. Pam and Bobby fight over J.R.'s attempts to ruin Cliff. Bobby learns about the Asian oil deal and the mortgages J.R. has taken out and tells Jock.
A typhoon delays drilling in Asia as J.R.'s loans become due. Cliff resigns from the Office of Land Management to run for Congress. Ellie makes a massive sacrifice to save Southfork and Ewing Oil, but blames J.R.
Sue Ellen's lack of interest in her baby causes tensions throughout the family. Jock scrambles for a way to stop drilling on Southfork. J.R.'s gamble with the Asian oil leases comes to an end and Jock makes a decision about the future of Ewing Oil.
J.R. tries to convince Jock to send Bobby back to Ewing Oil instead of coming back to work himself. Pam and Bobby fight over how much time she spends at the store. Pam gets a promotion. Ray gets back together with Donna Culver.
Most of the family goes to Colorado to visit Jock's first wife. J.R. stays behind to rig a deal on the Asian oil wells. Pam hires a detective to look into what became of her mother. Sue Ellen has trouble with the bottle again.