There are many ways to earn credits in Star Wars Galaxies, you can either buy SWG credits online from a trusted source, or take your time and earn it in-game. In the game, the fastest and easiest way to earn your creds is by doing missions. There are 2 types of missions: Delivery Missions and Destroy Missions. To get a mission, find a mission terminal in the city. Orange colored terminals are neutral missions while the blue ones are faction dependent with a corresponding faction flag next to them.
Delivery missions are good for starting characters to earn credits. They consist of delivering a package from one location to another. The delivery location might be in the same city or in another city. Delivery locations will always be marked with a waypoint which you can activate in your data pad (CTRL+D). The more farther the destination, the more credits you earn from the mission. If the destination is in another city, you will need to buy a shuttle ticket to get there. To do that, go to the nearest shuttleport using "/find shuttleport" . Then purchase a ticket to next city and wait for the shuttle, then get on it by using your ticket next to the shuttle.
Destroy missions on the other hand are far more difficult and are definitely not for starting characters. Destroy missions consist of going to a specific location/dungeon and having to kill certain NPCs/monsters. They are located outside of cities and are best done with parties. The credits earned on destroy missions is more, but you can earn more credits faster without getting any damage by doing delivery missions.
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