http://tvtropes.org/pmwiki/pmwiki.php/Main/GenerationalSaga

— John Adams, 1780 " I must study Politicks and War that my sons may have liberty to study Mathematicks and Philosophy. My sons ought to study Mathematicks and Philosophy, Geography, natural History, Naval Architecture, navigation, Commerce and Agriculture, in order to give their Children a right to study Painting, Poetry, Musick, Architecture, Statuary, Tapestry and Porcelaine."

This is a work that traces the evolution of a single family through multiple (usually three) generations, covering a long enough period of time that you get to see more than one generation at the same age or stage of life. Often it follows the pattern of Three Successful Generations:

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The first-generation protagonist is someone who has begun with a "fresh slate" (for instance, an immigrant to a new homeland). The second-generation protagonist builds on the first's foundations and establishes the family's position in the new world (The daughter who becomes entirely assimilated in the host culture and goes on to have a successful career). The third-generation protagonist reaps the benefits as a full-fledged member of society. (The grandson who ends up learning to appreciate their ancestral heritage).

With only two generations, the third-generation protagonist is usually the one omitted; works which follow this pattern through more than three generations might have multiple second-generation-type (assimilated) protagonists, or they might alternate between second- and third-generation-type protagonists.

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Another frequent theme is that the first- and third-generation characters have more in common with each other than either does with the second-generation character. Often they both react in the same way to her, or (if the first-generation character is still alive when the third-generation character is around) form a bond that excludes her.

This is not to say that this trope applies to only three generations. The stories can span decades, hundreds or even thousands of years, all following the same family.

Note that properly speaking this only applies to unified works; having a Changing of the Guard sequel in which we meet Generation Xerox isn't enough. It's primarily a literary trope, though it also appears in theater and film; you might be able to see less-planned versions of it in long-running Soap Operas or possibly even Comic Books (but with the latter, it's far more common for the first-generation character to live well beyond when the third-generation would reach adulthood).

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Compare An Immigrant's Tale. Also compare Three Successful Generations. May end up producing a Tangled Family Tree if the family is especially prolific, and most or all of the characters are plot-important.

Examples:

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Anime and Manga

Comic Books

Films — Animated

The movie American Pop covers four generations and their relationship to popular music in America.

When put together, The Lion King and The Lion King II: Simba's Pride are one. The first film is about a young lion cub named Simba going on a long journey of self-discovery and rising up to lead the serengeti after the murder of his father, King Mufasa. The sequel focuses on the forbidden romance between his daughter Kiara (the future queen) and the young, reluctant successor of his deceased Arch-Enemy.

Film — Live Action

The Godfather features Don Vito Corleone, his four children and several (mostly unnamed) grandchildren. Part II takes this further with its flashback storyline. Not only do we see the same characters from the first film (including those who are dead), but we also see Vito's mother as well as know her and his father and brother's ultimate fates. Bicentennial Man is about a robot who lives through three generations of the family he was made to serve, before finally falling in love with a member of the fourth generation as he gradually grew more human.

The movie Mi Familia, whose tagline is "Three generations of dreams."

The Star Wars movies have so far covered the adventures of four generations of the Skywalker family with Shmi, Anakin, Luke and Leia, and Kylo Ren / Ben Solo . The Legends Alternate Continuity did something similar with the Skywalker/Solo children and later Cade Skywalker and Ania Solo, distant descendants of the original characters.

. The Legends Alternate Continuity did something similar with the Skywalker/Solo children and later Cade Skywalker and Ania Solo, distant descendants of the original characters. Hellraiser: Bloodline follows three non-consecutive generations of the LeMarchand/Merchant family: Phillip LeMarchand in 1796 France, John Merchant in 1996 Manhattan, and Paul Merchant on a space station in 2127.

The 1999 film Sunshine tells the story of the Hungarian Jewish Sonnenschein family, with each generation living in a time of political upheaval. The first generation has to deal with World War I and its ramifications, the second generation with World War II and the third generation lives through communist Hungary.

The Rocky movies follow Rocky Balboa all the way from his days as a boxing champion in the 70s and 80s, to his days as a retired fighter mentoring the son of Apollo Creed, his deceased rival and friend. The movies also explore his relationship with his own son, Rocky Jr.

How the West Was Won follows the Prescott family and the next three generations of their descendants from 1839 to 1889 as they move increasingly further west to the Pacific Ocean.

Literature

Live Action TV

Theatre

The family from Rock 'n' Roll by Tom Stoppard aren't immigrants, but it does have the three generations of protagonists with the intermediate one being the odd one out. The Dolls of New Albion: A Steampunk Opera follows the McAlistair family through four generations; one for each act.

Tabletop Games

Video Games

Western Animation