Dexeter was the chief scientist of the Alzarians.
He based his facility inside the Starliner. He was fascinated by the nature of the Marshmen that made the Alzarians fear them. When a Marshchild was captured within the starliner it was taken to Dexeter, who began examining it.
Dexeter took tissue samples for which the Fourth Doctor berated him. However he did not listen and, after permission from the Deciders, began a full examination. However as he was about to make the first incision to the Marshchild's head, it awoke through a telepathic link to Romana II.
The Marshchild strangled Dexeter to death. The Doctor used tissue samples from Dexeter while comparing Alzarian, Marshman and Alzarian spider cell structure. This revealed they were all the same. (TV: Full Circle)
As Decider Draith was being pulled into the swamp at Mistfall, he told Adric to "tell Dexeter we've come full circle". During his testing of the Marshchild, he claimed it was for the greater scientific good. (TV: Full Circle)