Nightmare Police

The Nightmare Police (ナイトメアポリス) is a group composed of two Reploids, Bit and Byte, formed by Dr. Doppler to protect Dopple Town.

Mega Man X3
After two Mavericks are defeated, the Nightmare Police begin hunting X. They have a chance to appear in the empty sub-boss rooms across any of the eight main stages for a fight with X. If the Nightmare Police do appear, a boss fight is initiated with either Bit or Byte. After defeating them, they flee and are not encountered again until Doppler's Laboratory, where they fuse to become Godkarmachine O Inary. However, if X manages to defeat them with one of their weaknesses, they will be destroyed on the spot and will not reappear in Doppler's Laboratory. If both Nightmare Police are destroyed in this manner, the fight with Godkarmachine O Inary will be replaced by a fight with Press Disposer instead.

Rockman X3 manga
The Nightmare Police are two Reploids upgraded to have their bodies made entirely of Worms, granting them great power and allowing them to dismantle their bodies and move like Worms. Dr. Doppler only sees them as experiments, having no attachment to them and attacking them alongside X due to them being on his way. As they survived, Doppler decided to use Worms to upgrade them into "a powerful tool", turning them into Godkarmachine O Inary against their will.

Rockman X Giga Mission
Isoc studied Dr. Doppler's works related to the Limited and upgraded it, now calling it the Extreme. He then created two Reploids from data of Doppler's Nightmare Police and the Extreme, Sakitira CC and Pranara DD, and ordered them to search for Zero.