Abstract: A long-standing problem in particle physics is how to identify anomaly-free sets of chiral
fermions charged under one or more U(1) gauge symmetries. I will present the general
solution to the anomaly equations for any number of fermions charged under a single U(1).
Then I will discuss the general solution for six fermions charged under a U(1)XU(1) gauge group,
and give an example of a dark matter model based on that solution. Finally, in U(1) extensions
of the Standard Model, I will derive the general set of charges for three right-handed neutrinos.