With Heavy Fighting and Significant Romance:
* Inuyasha: This classic series has intense demon-fighting and a multi-layered romance between Inuyasha, a half-demon, and Kagome, a modern girl transported to his world.
* Bleach: With over 366 episodes, Bleach boasts thrilling battles, complex character relationships, and a few central romances, particularly between Ichigo and Rukia.
* Fairy Tail: This long-running series features an epic battle system alongside numerous interwoven romances. The focus shifts between fighting and relationship drama depending on the arc.
* Fruits Basket: While not as battle-heavy as the others, Fruits Basket has a strong focus on character development and romance, with some supernatural fighting sprinkled throughout.
Longer Series with Focus on Romance and Some Fighting:
* Ouran High School Host Club: This lighthearted series features comedic situations and a sweet romance, with only occasional bouts of fighting.
* Kamisama Kiss: This supernatural rom-com has a fair amount of fighting, but the emphasis is on romance and character development.
* Sailor Moon: A classic with many battles, but the romance and relationships between the Sailor Scouts play a major role in the story.
Important Note: Even in series with significant fighting, romance might not be the primary focus or it might be more subtle and slow-burning than you're looking for.
Before you dive in, I recommend watching a few episodes of each series to see which one best suits your preferences!