This work deals with the problem of detecting and estimating multiple radar targets present in the same range-azimuth resolution cell of a surveillance radar system with a mechanically rotating antenna. In the first part of the work, we tackled the problem of estimating target complex amplitudes, Doppler frequencies, and directions of arrival, and a consistent estimator based on the asymptotic maximum likelihood (AML) method was derived. In this second part, we tackle the "detection problem," which consists of determining the number of targets. First, the target parameters are estimated, assuming a maximum number of possible targets. Subsequently, these estimates are used in a successive hypotheses test procedure. The statistic of the test at each step of the procedure is derived by using an asymptotic expression of the generalized likelihood ratio test (GLRT) statistic. Performance of the proposed algorithm is investigated through both asymptotical analysis (as concerning the probability of false alarm) and Monte Carlo simulation.