Garryn Bek was a law enforcement officer on Cairn, a world notorious for its corruption and drug trade. In its heyday, a large portion of the illegal drugs distributed in the area were grown on Cairn. Likewise, its population had the highest addiction rate of any known world — approaching 100% in some areas. The police force that Bek belonged to was completely under the control of drug lords, who were headed by Kanis-Biz, Garryn's father-in-law.
When the Dominators swept through the galaxy seeking support for their plan to attack Earth, many worlds offered up their citizens as collateral of sorts. By surrendering its people, Cairn like many other worlds showed their compliance (or at the very least noninterference) with the Dominators' plans.
His father-in-law was only happy to offer Bek as Cairn's prisoner. He was taken to the Starlag prison, where he befriended some of the other captives. The Starlag soon turned out to be the focal point for a rebellion against the Dominators, led by Adam Strange and the devious Vril Dox II. (Invasion! #1-3) Bek then joined Dox, along with the Durlan, Stealth, Lyrissa Mallor of Talok VIII, and Strata of Dryad in helping to defeat the Dominators' plot in space.
After their victory, the band of exiles accompanied Dox to his home world of Colu. They were successful in shutting down Colu's Computer Tyrants. But without the Tyrants to guide it, Coluan society practically self-destructed. (L.E.G.I.O.N. #1-3) Dox unwittingly became a sort of "godfather" to his people, which gave him the idea to form a new police force to replace the former Green Lantern Corps. Bek and the others were hesitant at first to join Dox, but ultimately decided that it might be a good idea to stick around, if for no better reason than to keep an eye on Dox.
Garryn Bek questioned his place alongside so many powerful individuals, but Dox's next decision ensured Bek's continued involvement. Dox decided their next mission would be to eradicate the drug trade from Cairn, and he sent their newest recruit, Lobo, to assassinate Kanis-Biz! Once they arrived, Bek led a party to try and stop Lobo, but this was Dox's plan. Meanwhile, Dox and Lobo crippled the police force and secured their allegiance. (#5) Bek and the others tried unsuccessfully to prevent Biz's assassination, and Lobo broke both of Garryn Bek's legs. (#6) Dox and Lobo then finished off the remainder of Cairn's opposing drug lords. (#7)
Garryn kept the secret from his teammates. They did not meet his wife, Marij'n Bek (Kanis-Biz's daughter) until by strange circumstances, Stealth killed Dox. Marij'n Bek showed little remorse for her father's passing and was a highly accomplished scientist on Cairn. She was able to clone Dox and restore his memories as well. As for her marriage to Garryn, it was by that point a sham. Marij'n was overweight and had become increasingly insecure. Despite this, she admitted that she still loved Garryn and was open to the second chance they'd been given. (#8-9)
Soon Dox's organization began to grow and take on contracts to protect other worlds. The team was named L.E.G.I.O.N. (Licensed Extra-Governmental Insterstellar Operatives Network), and Garryn and Marij'n became integral parts of its core. Marij'n welcomed the opportunity to do good work with some (mostly) honest people for once.
In space, Garryn ran afoul of the legendary Emerald Eye of Ekron in orbit above the planet Rishta. The Eye killed members of his crew then stopped short of killing Bek himself. For whatever reason, the Eye chose Bek as its new "beholder." Bek now had near-unlimited power at his disposal — if he could control it. When he returned to Cairn, the Eye was already influencing his actions and it caused him to lash out at his teammates. Finally, Dox stared down the Eye and it backed off. (#10-13)
Dox instructed Marij'n to find a way of siphoning power away from the Eye, but no one could predict the result: the Emerald Eye instead made Marij'n its "co-beholder." In the process, it transformed her body, making her thinner. (#17)
The Eye during this time period was fickle, though. Not long after adopting her, it abandoned Marij'n Bek for good. (#22) Soon, it left Garryn as well and was not heard from again. (#26)
But Marij'n's physical transformation gave way to changes on the inside. Perhaps it was fate, because she soon met the man who'd become new love of her life: the legendary hero, Captain Comet. (#24) After this, Marij'n no longer had any desire to work on her marriage, and denied Garryn's advances. (#27)
Comet and Marij'n became friends right away, and they stood together to oppose Dox when he planned to brainwash young Lydea Mallor. (#25) She and Comet officially joined the team as core members together. (#29)
Meanwhile, Garryn immersed himself in the administrative duties of the L.E.G.I.O.N., restructuring it into smaller units. But he was not so busy as to be blind. He noticed the chemistry between his wife and Captain Comet and hesitantly gave Comet his "blessing" to pursue a relationship with Marij'n. (#40)
Marij'n's happiness was delayed when Captain Comet fell prey to an alien parasite, which took complete control of him. Comet broke off his relationship with Marij'n. To protect Marij'n, he lied and claimed that his actions had been those of the alien inside him. (#45-48)
Soon after this, Comet was attacked again by the parasite and the team assumed that he was dead. (#63)
The L.E.G.I.O.N. was eventually overtaken by Dox's son, Lyrl, who brainwashed most of the team into his service. Marij'n an Garryn were among those under his thrall, while several others escaped.
To her great credit, Marij'n began to figure out Lyrl's mind control methods and she managed to free dozens of planetary leaders from Lyrl's mind control. (REBELS #7-9) Around this time, Captain Comet also returns to Cairn from the dead; he was completely unaware of the recent changes. (#10)
He saved Marij'n just before Lyrl could mind wash her as well. Dox eventually managed to disable Lyrl, and in the aftermath, Captain Comet assumed leadership of the L.E.G.I.O.N. Garryn and Marij'n returned to active duty. (#17) At some point after this, Dox reassumed his leadership of the L.E.G.I.O.N. and relocated their headquarters to the planet Malthus.
Garryn has continued to serve with the L.E.G.I.O.N. Marij'n's course, and that of her relationship with Captain Comet has not been revealed. She and Garryn had never officially divorced. (Infinite Crisis #1)