Caleb Swain, one of the wealthiest and most famous men in the U.S., receives news at the hospital maternity ward that his wife, Letitia, has given birth to twins. However, Caleb is horrified when he sees the newborns’ grotesque appearance. He is unaware that the children are the result of an extraterrestrial intervention. Worried that humans will destroy Earth’s resources and threaten the galaxy, aliens have sent the twins as advisors, with the intelligence to solve the planet’s problems. Previously, the aliens dispatched a set of extraterrestrial twins to China, enabling that country to become the world’s most advanced culture with the ability to miniaturize humans. However, the Chinese also have ambitions to control gravity and dominate the planet. Concerned about a dangerous imbalance of power, the aliens recall their advisors in China and hope that the American twins will spearhead a more peaceful solution. The Swains’ family physician, Dr. Frankenstein, conceals the twins, Wilbur and Eliza, from the public and sets up a care facility at a mansion, staffed by a thirty-member team, who look after the “baby monsters,” as Caleb and Letitia Swain continue their lives without any direct involvement other than financial support. Meanwhile, the Chinese discover the existence of the ugly twins. Believing the Swain children are another specimen of exceptional intelligence, they send agent Lum Fung to spy on the duo, and Fong convinces Dr. Frankenstein to hire him as the children’s cook. Fifteen years later, Wilbur and Eliza remain isolated at the mansion. When the miniaturized Chinese ambassador Ah Fong reveals to the Swains that the twins are geniuses, Caleb and Letitia prepare to visit their children for the first time. Meanwhile, Wilbur and Eliza conclude that humans strive to be as dumb as possible after observing their servants, who are consumed with partying and drinking champagne. In an effort to fit in, the twins pretend to be mentally challenged while hiding their theoretical writings. Sylvester, the butler, halts the staff’s carousing and quickly organizes a cleanup of the mansion after receiving news about the Swains’ arrival. Caleb and Letitia invite the U.S. President to meet the children based Ah Fong’s prediction that Wilbur and Eliza are a great resource for the planet. However, the Swains and the President are shocked as the twins act like imbeciles and speak gibberish. Sylvester uses a can of mace to control the children’s antics, while Caleb and Letitia believe the Chinese have deliberately misled them. Overhearing their parents’ disappointment, Wilbur and Eliza change into adult clothing and reveal their intelligence. Dr. Frankenstein separates the twins to administer I.Q. tests, but Wilbur and Eliza perform poorly without each other’s company. The twins demonstrate that if they rest their heads together and embrace, their brainpower is optimized. Letitia, however, views the behavior as incestuous and the twins are placed in straightjackets. Wilbur is sent to a military academy, while Eliza stays at the mansion. Meanwhile, despite the setback, the aliens remain patient about their plan. The Chinese agent Lum Fung continues to spy on Wilbur while working as a drill sergeant at the academy. As Wilbur is trained to forget his sister’s name, Eliza becomes more depressed without her “missing half.” Sylvester, who previously dismissed the children as spoiled imbeciles, now has sympathy for them. One night, Eliza receives a visit from ambassador Ah Fong, who is anxious for the twins to reunite and help solve the problem of controlling gravity. He reveals Wilbur’s location and Eliza arrives at the academy to find her brother receiving shock treatment. She rescues him and carries him away. Colonel Sharp, the school’s leader, sends a posse of armed men with dogs to find the twins. When Wilbur finally regains consciousness, the twins’ intelligence returns as they place their heads together. Back at the mansion, they lock themselves in the dining room, which is encased in steel, to concoct their gravity theories. Sharpe decides not to dynamite the doors as he and Dr. Frankenstein try to talk the twins into surrendering, but the children fear being separated again and refuse. As Wilbur and Eliza get closer to controlling gravity, the Chinese ambassador arrives through the room’s chimney in his miniature flying machine and orders the twins to continue working on their equation in China or face destruction. Embracing each other, the twins reject his offer and Fong’s men aim their weapons. Suddenly, the room shakes as aliens arrive to take Wilbur and Eliza home. The children are welcomed by their species, who state that earthlings remain too afraid of the unknown to benefit from the twins’ superior wisdom. Boarding a spaceship, Wilbur and Eliza wave goodbye to their parents, and Sylvester smiles as they leave.