The structural behavior of Np2Co17 is investigated by means of high-pressure diamond-anvil compression measurements and is compared with that of the isostructural compounds Lu2Co17 and Lu2Ni17. The Th2Ni17-type hexagonal crystal structure is preserved with no measurable discontinuous volume collapses up to the highest achieved pressure, p = 43 GPa. For Np2Co17, fits to the Birch-Murnaghan and Vinet equations of state give values of the isothermal bulk modulus and its pressure derivative of B-0 = 286 GPa and B-0' = 3, revealing that this Np compound is a highly incompressible solid with stiffness comparable to that of superhard covalently bonded materials. For the Lu2T17 (T = Co, Ni) compounds, the measured bulk modulus changes from B-0 = 137 GPa for T = Co to B-0 = 257 GPa for T = Ni. The isothermal equation of state for the studied compounds are in excellent agreement with the results of ab initio fully relativistic, full-potential local spin-density functional calculations. Theoretical estimates of the bulk modulus are given also for Np2Ni17, for which B-0 is predicted to assume values intermediate between those measured for Lu2Ni17 and Np2Co17.