Brock caught Mudkip in A Mudkip Mission. Mudkip lived at a pond where a number of Mudkip were bred. While most of the Pokémon left the pond as they grew older, the one that Brock caught was already mature and acted as a guardian of the younger, smaller Mudkip. It joined Brock and left the pond after he helped it rescue itself and the younger Mudkip from a Team Rocket attack.
In A Chip Off the Old Brock, Mudkip evolved into a Marshtomp during a training battle versus Ash's Grovyle. It then became smitten with a Flaaffy, as Brock was smitten by its trainer.
Marshtomp is among the more behaved of the gang's Pokémon. It is often seen helping Ash's Pikachu break up scuffles between Pokémon. Being a Template:Type2 Pokémon, it usually worked with Brock's Ludicolo to launch double Water Gun attacks. It is also called upon to search for things underwater. It is also often used to help track down a missing Pokémon or object (usually due to Team Rocket stealing it) using the fin on its head as a radar.
Brock left his Marshtomp at the Pewter Gym when he decided to join Ash in the Sinnoh region.
Out of the main characters' Hoenn starter Pokémon, Marshtomp is the only one that didn't fully evolve.
Before Brock captured Marshtomp (as a Mudkip), it acted tough to protect Old Man Swamp's Mudkip, similar to Ash's Bulbasaur who protected a village of Pokémon from intruders.
Out of all Pokémon belonging to the main cast, Mudkip took the longest to evolve while its Trainer was continuously part of the main cast (May's Squirtle and Bulbasaur were revealed after her 76-episode absence, Brock's Zubat evolved after Brock's return from his Orange Islands absence, Misty's Togepi evolved after Misty's 45-episode absence, Ash's Phanpy evolved after he picked it up at Professor Oak's lab near the end of the Advanced Generation series (having been hatched in Johto), and Brock's Onix evolved under his brother's care).
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For more information on this Pokémon's species, see Mudkip and Marshtomp.