The series chronicles the rocky coexistence of Larry Appleton and his distant cousin Balki Bartokomous. A Wisconsin native, Larry, who comes from a large family with numerous brothers and sisters, has just moved into a new apartment in Chicago, and is experiencing his first joys of newfound privacy when Balki, a hitherto unknown cousin from a Greek-like island in the Mediterranean called Mypos, drops by to live with him. Balki, a shepherd by trade, interprets what little he knows about the United States by relying on his own recollections of American pop culture, which are often out-of-context. After initially gently rebuffing his cousin's request to stay at his apartment, Larry, an aspiring photographer, decides to take Balki under his wing and teach him about American life...
Larry is miserable on his 24th birthday after he blew a photo opportunity. So Balki tries to throw him a last minute surprise birthday party for him to cheer him up.
Jennifer asks Larry if he can call a plumber for her to fix her shower head while she's away. Larry decides that to impress her he'll fix it himself and as Larry and Balki try and put everything together, things go extremely wrong and they end up flooding Jennifer and Mary Anne's bathroom.
Jennifer was asked out on a date by an old boyfriend and checked with Larry first. But he agreed thinking that's what she wanted but she really wanted to know here their relationship is going. Confused, She breaks up with Larry who is too scared to tell her how he really feels but they eventually end up getting engaged.
Larry decides to join a health club after having the hots for a member named Jennifer. But he thinks she's only interested in jocks and pretends to be one. Balki goes with him and picks up a woman right away who happens to be Jennifer's best friend Mary Anne.
As the best man at Larry's upcoming wedding, Balki is tricked by Mr. Gorpley into throwing a bachelor party and when Mr. Gorpley show up at the party, he spikes the punch and hires a stripper and Jennifer finds out.
Balki wants to get his driver's license but Mr. Twinkacetti doesn't think he can do it. But Larry is so confident that he can, that he bets $50 and offers Balki his car.
After the river takes them on a wild ride, The four end up lost in the woods. Hoping that Larry can regain Jennifer's respect, he talks Balki into letting him lead them back to the camp site but they end up walking for five hours in a circle. Later, Larry and Balki almost drown in quicksand and in the evening, they get attacked by a bear.
According to a sacred Myposian custom, Balki and Mary Anne must be married within 24 hours and they get everything ready. Larry feels left out of the duties so Balki makes him his best man and the guardian of his Myposian marriage necklace which he must have during the ceremony, but Larry accidentally throws it out. So Larry and Balki search the dump for it and eventually find it and Balki and Mary Anne finally get married.
Larry and Balki get part time jobs to earn extra money. Balki tries stuffing teddy bears, but Larry asks for his help with door to door selling cleaning products. However, Larry is determined to go to a mansion and sell lots of products instead of going door to door with disastrous results.
Jennifer's mother comes to town and wants to meet Larry, and Jennifer doesn't think that her mother will approve of her marrying him. Later on, Larry falls down the stairs at the Chronicle and gets amnesia which last during the dinner where Larry meets Mrs. Lyons.
Larry has a date with a beauty queen but after going to the hospital to visit Mr. Twinkacetti (who has broken his leg), he catches a cold and when Balki tries to cure him with a secret Myposian cure, he ends up sleeping for three days.
Larry decides to impress Mr. Wainwright by enlisting himself and Balki to move his brand new oversized couch up the elevator to his office while the elevator is under repair.
Larry goes to an auction to cover a story and brings Balki with him and Larry demonstrates the bidding procedure at an auction and they wind up buying a very expensive bottle of wine for $21,000. They now must hide it from Jennifer until they can go back to the auction and resell it.
Balki hasn't been sleeping due to a nightmare that has been haunting him about him not being able to help out at harvest season back on Mypos.
Lydia is miserable when her boyfriend dumped her so Balki uses his match-making skills to fix Lydia up with a man who turns out to be a gigolo who married wealthy women, takes their money and leaves them.
On Balki's 25th birthday, his mama has a pre-arranged marriage that Balki must go through with, even though he is in love with Mary Anne. So Larry and Jennifer try and find a way to save Balki from being unhappy.
When a big corporation in Chicago wants to buy 300 acres of land on Mypos, Balki was chosen to negotiate the sale, and he picked Larry to guide him through. When they are offered 10% of the total sale of 28 million dollars, Larry insists they accept is but Balki has a funny feeling about it.
While playing a board game, an argument breaks out between Jennifer and Mary Anne. The result being Mary Anne moving out and in with Larry and Balki at Balki's insistence. Larry doesn't like the idea because is jeopardizes his relationship with Jennifer. So Larry and Balki devise a plan to get Jennifer and Mary Anne back together.
Balki runs for student body president and lets Larry help and as usual, Larry goes completely over the top. The students however, don't like the idea of Balki's idea of reinstating the language requirement so Larry thinks Balki should lie in order to win but he won't.
Larry suggests to Mr. Wainwright that a Chronicle employee stay on a billboard until the Bull' losing streak is over. Mr. Wainwright liked the idea and assigned Larry to find someone to do it. So he tricks Balki to do it but when Balki wants to get down, Larry kicks the ladder down and they both get stuck up there until the Bulls win.
Balki and Mary Anne expect Larry and Jennifer to set a wedding date but they're too scared. To help them, Balki gives them an official marriage test to see if they're right for each other but things don't go as expected. In the end they set the wedding for September regardless of what the test says.
Larry has been invited to a formal party for a photographer he idolizes but Balki's honest opinions embarrass Larry.
Balki insists on buying a lottery ticket but Larry thinks that it is just a waste of money for something that can't possibly win. But during the draws, Larry realizes that Balki picked the right numbers and won 28 million dollars but Balki can't remember where he hid the ticket.
Balki manages to graduate night school at the top of his class but soon finds out that there is no graduation ceremony. So Larry talks to the principal and arranges one.
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