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This paper concerns the joint multiframe sequential target detection and track estimation in early-warning radar surveillance systems. The rationale for applying sequential procedures in such a scenario is that they promise a sensitivity increase of the sensor or, alternatively, a reduction in the time needed to take a decision. Unlike previous works on sequential radar detection, the attention is not restricted to stationary targets, namely position changes during the illumination period are allowed. Starting from previous sequential rules, different truncated sequential strategies are proposed and assessed: they are aimed at orienting the sensor resources towards either the detection or the track estimation or the position estimation. Bounds on the performances of the proposed procedures in terms of the system parameters are derived and computational complexity is examined. Also, numerical experiments are provided to elicit the interplay between sensor-target parameters and system performances, and to quantify the gain with respect to other fixed-sample-size procedures.