Both co-propagating and counter-propagating compressional Alfvén eigenmodes (CAE) are relatively ubiquitous in NSTX plasmas with toroidal field strengths of ⩽4.65 kG, but are largely absent in the NSTX-U plasmas with toroidal fields of 5.7–5.9 kG. In this paper we will study the co-propagating CAE. We show that the co-propagating CAE are seen with frequencies 0.4 ωci ⩽ ωCAE ⩽ ωci (with the exception of a few unique shots), that toroidal mode numbers are relatively high, ranging from 6 ⩽ n ⩽ 17, and that for plasmas with toroidal field greater than about 3.8 kG, are present for ≈2 < Vbeam/VA < ≈ 4 where Vbeam is the maximum injected beam velocity and VA is the core Alfvén velocity and Vbeam/VA is a crude measure of the fraction of beam-ions capable of resonantly exciting Alfvénic modes. Empirically, the prevalence of CAE activity increases for Vbeam/VA > 2 which is consistent with the relative lack of CAE in the NSTX-U plasmas from the Btor ≈ 5.9 kG shots which typically have Vbeam/VA < 2. These results suggest that CAE may be largely absent in ITER where Vfast/VA < 2 is expected, but may still be present in proposed ST-based fusion devices similar to ARIES-ST or CTF (Tillack et al 2003 Fusion Eng. Des.65 215, Voss et al 2008 Fusion Eng. Des.83 1648). There is a weak empirical scaling of toroidal mode number with toroidal field. We explore the nature of the fast-ion resonances with the simple linear eigenmode code CAEk. Calculations with the CAEk code reasonably match the experimental frequencies. From the calculated eigenmodes we find that 0.5 < < 1. While calculations of fast-ion drive are beyond the capabilities of this code, by coupling the CAEk code to a simple full-orbit code for the fast-ions we can estimate that the co-propagating CAE are primarily resonant with beam fast-ions with energies below ≈30 keV and that there are typically several strong resonances for each mode. We show that the fast-ion distribution as calculated with TRANSP has gradients at the resonant fast-ion parameters potentially capable of providing drive for the modes.