We investigate monitoring tests for bubbles. We extend the sup-ADF and generalized sup-ADF tests by Phillips, Wu, and Yu (2011) and Phillips, Shi, and Yu (2015) to the monitoring scheme. We also consider applying the CUSUM detector as proposed by Homm and Breitung (2012). We derive the limiting distributions of the detectors under the null hypothesis, the moderate deviation alternative, and the local alternative. We find that although the moderate deviation alternative gives the difference in the divergence rates of the ADF-type and CUSUM-type detectors, the local asymptotic theory is more useful to understand their difference in details. We also conduct the finite sample simulations and confirm that the local asymptotic theory approximates the finite sample properties of the test very well.