Aiming at the range-spread target detection problem in KK-distributed heavy-tailed radar clutter, the KK-distributed radar clutter was taken as a spherically invariant random vector. The Neyman-Pearson optimal integrator for the range-spread target detection with known target amplitude was derived firstly. Then by replacing the ideal target amplitude with the maximum likelihood estimates, the detector model in generalized likelihood ratio test (GLRT) was obtained. Both of the detectors are dependent on the modified Bessel function of the second kind, which makes the detectors computationally complicated, so a suboptimal generalized likelihood ratio detector based on order statistics (OS-GLRT) was proposed. The OS-GLRT takes some range unit echoes with largest amplitude in detection window as target echoes. The performance assessment conducted by Monte Carlo simulation validates that: the optimal integrator and GLRT have better performance, however, they are hard to applied, and the OS-GLRT is a more practical detector.