The Advanced Hydrotest Facility (AHF) proton synchrotrons are likely to use parallel-biased, Nickel-Zinc ferrite cores in accelerating cavities. The Booster frequency is anticipated to be in the range of 0.32 - 1.25 MHz, depending on the choice of final energy and design, while the 50 GeV Main Ring (MR) frequency range is 4 -5.03 MHz. Experiments were conducted to characterize the response of large rings of Ferroxcube 4M2, 4B3 and 8C12 ferrites over these frequency ranges. Testing of 4M2 for the Booster revealed degraded performance due to the nonlinear response of incremental permeability at elevated flux densities. This constrains the operating voltage to a range well below the thermal power limits of the material. The 4M2 and 4B3 material appears to be satisfactory for the MR. The 8C12 material is satisfactory for the Booster if it is operated below the threshold of a high loss effect. The final cavity designs will be based upon the results of ferrite measurements from the test cavity, for the requirements of the AHF accelerators. Testing methods, analysis and results will be presented.