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 gets a job at the Chicago Chrinicle local newspaper as a reporter and brings Balki to find a job. Mr. Burns the city editor hires Balki in the mail room but Mr. Gorpley the mail room boss doesn't want him there and tries everything to fire him.
When Larry discovers that he has gained 7 pounds, He goes on a diet that won't work. So Balki gives him a Mypos diet but Larry has trouble following it and Balki won't let him quit.
The editor of the Chronicle's Sunday Magazine makes a play for Balki but he isn't interested. She won't take no for an answer and anyone who ever tried to report her lost their jobs.
Balki buys one share of stock in a cereal company and discovers that there isn't enough raisins in a box that they advertise. Knowing that the company is cheating the public, he decides to go to head office to complain and Larry goes with him.
While grocery shopping, Balki wins a shopping spree to happen the next day and he thinks it would be fun. But Lary makes a plan to get certain things to sell for an air conditioner which takes all the fun out of it.
Jennifer is planning on buying a surprise typewriter for Larry and asks Balki for help barganing at a clearance sale. Larry gets suspicious after he sees Balki and Jennifer sneaking around, and thinks they're having an affair.
When a famous psychic visits the Chronicle, She goes into a trance and predicts that a bog storm will come and Larry will die at midnight after sitting on a sheep and eating a golden ring. Larry thinks that it is just superstition until a storm comes out of nowhere.
While at a happy hour restaurant, Larry and Balki get beaten up at a bar by a bully who hit on Jennifer. So they decide to take karate and after several weeks of fine training, Larry insists on returning to the bar to pick a fight with the bully.
Balki is cheated by a con artist who sold him counterfiet watches. And after getting no help from the police, Larry and Balki go undercover to expose the con artist and put him out of business.
Jennifer has been given a promotion but if she accepts it, she has to move to LA. Larry refuses to tell her how he feels as a fear of rejection but later that evening, he has a dream about being a lonely old man with Balki and Mary Anne married, rich, living upstairs.
When Larry and Balki get cable TV, Balki becomes glued to the TV and won't stop watching it to the point where he forgets about his job, sleep, and never goes out anymore. So Larry must make an important decision of getting rid of the cable.
Balki accidently delivers Larry's offensive article to the publisher. So they break in late at night to retrieve it and end up on the ledge dealing with someone trying to commit suicide.
When Larry and Balki are chosen to be in the commercial for the Chicago Chronicle, Larry takes his acting abilities too far and goes overboard.
After Mr. Gorpley gets information out of Balki about what's in the mail, Larry tells him that it's against the rules for him to give away what's in the mail. But in order to buy his dream car, he needs to know about his raise that was processed in the mail.
Vince Lucas the racketeer that Larry and Balki testified against has been paroled and Balki invites him into their apartment after writing to him ever since he went to prison. Even though he threatened them, Balki trusts him but Larry's too scared.
After Balki serves Larry, Jennifer, and Mary Anne some ""bibi-bobkas"" (Mypoian cream puffs), Larry suggests selling them but baking them cannot be rushed.
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.
Balki is excited because his 106 year old grandmother Biki is coming to America to see him but when she switched planes in New York, she died at the airport and Balki has a hard time accepting it and pretends to be happy.
Balki manages to graduate night school at the top o his class but soon finds out that there is no graduation ceremony. So Larry talks to the principal and arranges one.
Larry is very angry at Balki for making him late for work and won't speak to him so Balki handcuffs them together and loses the key during Larry's important luncheon sate with Mr. Burns and the publisher R.T. Wainwright.
Larry's successful brother Billy (Ted McGinley) comes down for a visit, and Larry is upset because he brags about his success. So he tricks Balki into lying to Billy to make him think Larry is more successful.
While Larry is doing some important research, Balki goes out to the races and when he gets back, he tells Larry about meeting Carl Lewis but Larry doesn't believe him since he has taken Balki's money and left.