A traveling-wave resonator is presented which is created by the radial arrangement of two or more branches of coupled positive-index/negative-index guides. In each branch, a microstrip line (representing the positive-index line) is coupled to another microstrip line which is loaded with series capacitors and shunt inductors (representing the negative-index line). This resonator features some distinct properties. It exhibits multiple resonant frequencies and their number increases with the number of branches. In contrast to the traditional traveling-wave resonator, these resonant frequencies are not harmonically related. At each resonant frequency, the electromagnetic fields are stronger at the connection point and exhibit exponential decay along each branch. Moreover, the performance of the coupler can be made independent from the length of the branches. This resonator can be employed in multiband antennas, sensors and filter applications.