Compact double notch coplanar and microstrip bandstop filters are described. They are based on a version of the open interconnected split ring resonator (OISRR) integrated in microstrip or coplanar waveguides. The OISRR introduces an RLC resonator connected in parallel with the propagating microstrip line. Therefore, this resonator can be modeled as a shunt circuit to ground, with the R, L and C elements connected in series. The consequence for the frequency response of the device is a notch band at the resonant frequency of the RLC shunt circuit. The number of notch bands can be controlled by adding more OISRRs, since each pair of rings can be modeled as a shunt circuit and therefore introduces an additional notch band. In this paper, we demonstrate that these additional rings can be introduced in a concentric way in the same cell, so the size of the device does not increase and a compact multi-notch bandstop response is achieved, with the same number of notch bands as pairs of concentric rings, plus an additional spurious band at a higher frequency.