In this paper, we study the online scheduling problem
on two uniform machines with speeds 1 and $s \geq 1$, in which jobs are arriving over
time. We consider both the preemptive and the non-preemptive machine environments.
We first present a 2.618-competitive algorithm
for the non-preemptive setting with the objective to minimize the total completion times.
In the preemptive setting with the objective to minimize
the total weighted completion times, we give an online algorithm
which has a competitive ratio of 2.