This paper addresses the problem of early detection of K >=1 multiple moving targets in radar systems through the use of track-before-detect (TBD) techniques. Assuming prior knowledge of K, a binary generalized likelihood ratio test (GLRT) is first derived, which shows that the multi-target TBD problem can be regarded as a K−path trellis search. Next, a novel multi-hypothesis test strategy is presented for K unknown as the solution of a constrained optimization problem, which subsumes the convectional binary GLRT. Both optimal and sub-optimal implementations of the proposed TBD strategies are discussed which allow to trade better detection and tracking performances with a lower computational burden. Numerical examples are also provided and commented.