The accident was the conclusion to an away mission to collect some orchid samples. Only one molecular pattern rematerialized, and formed a healthy organism combining everything regarding Tuvok and Neelix, including organs, enzymes, and memories. According to the Doctor, Tuvix also possessed: "...Tuvok's sense of intellectual superiority, and Neelix's annoying ebullience." Despite repairs having just been made to the transporter, no fault could be found in the logs at the time of the accident.
It was Tuvix, the name the combined individual had given himself, who realized what had happened. The plant samples, which were also caught up in the matter stream and were also a part of Tuvix, contained lysosomal enzymes. Tuvok's research indicated that this could be an indicator of Symbiogenesis, where an organism reproduces by merging with a second species to produce a hybrid. This usually only occurs with microcellular organisms. Tuvix suggested that being deconstructed during beaming allowed the symbiogenesis enzymes of the plant to react to Neelix's and Tuvok's DNA in the matter stream, so only the single organism existed at the point of rematerialization. The theory turned out to be correct when two plants and the orchid were beamed up together, resulting in one plant arriving on Voyager.
The Doctor told Tuvix that it may be many years before he could find a way to separate them - in the meantime, Tuvix was invited to become a member of the crew, and given the rank of Lieutenant.
Captain Janeway noted in her personal log that Tuvix managed to gain friends among the crew in his own right, and was a very able tactical officer who wasn't afraid to voice his opinion. To Janeway personally, he was an able advisor who cleverly used humor to make a point. His food was also seen as better than Neelix's. She also noted, however, that he was keeping a respectful distance from Kes, who was mourning the loss of two friends, and feeling uncomfortable with the reminder of them walking around who was yet someone different. Tom Paris joked, after Chakotay lost at pool against Tuvix again: "We've created a monster!"
It took the Doctor almost a month, but he found a way to reverse the accident, by using a radioactive isotope which would attach to the DNA strands of one of the merged species, but not the other. By beaming out the segregated DNA strands, the transporter would have the original DNA strands necessary to restore the two individuals.
Tuvix announced that he didn't want to die, and was happier combined than they had been separated. He pleaded with Kes, among others, to speak to the Captain on his behalf. Kes persuaded Janeway, however, that the procedure was necessary, as she needed Tuvok and Neelix. Tuvix pleaded with the bridge crew to stop the Captain from "murdering" him, but eventually allowed the procedure to take place, saying that everyone would have to live with his death on their conscience, for which he was sorry, as they were all, in his eyes, good people, his friends.
However, the Doctor refused to perform the procedure; as a physician, he had sworn an oath to do no harm, and refused to take Tuvix's life, especially against the will. Janeway herself, therefore, performed the process. It was a success, and Tuvok and Neelix were restored. (VOY: "Tuvix")