Multiple-quantum magic angle spinning (MQMAS) and satellite-transition magic angle spinning (STMAS) are two well-known techniques for obtaining high-resolution, or "isotropic", NMR spectra of quadrupolar nuclei. It has recently been shown that dynamics-driven modulation of the quadrupolar interaction on the microsecond timescale results in linewidths in isotropic STMAS spectra that are strongly broadened, while, in contrast, the isotropic MQMAS linewidths remain narrow. Here, we use this novel methodology in an 27Al (I = 5/2) NMR study of the calcined-dehydrated aluminophosphate AlPO-14 and two forms of as-synthesized AlPO-14, one prepared with isopropylamine (C3H7NH2) as the template molecule and one with piperidine (C5H10NH). For completeness, the 31P and 13C (both I = 1/2) MAS NMR spectra are also presented. A comparison of the 27Al MQMAS and STMAS NMR results show that, although calcined AlPO-14 appears to have a rigid framework structure, the extent of motion in the two as-synthesized forms is significant, with clear evidence for dynamics on the microsecond timescale in the immediate environments of all four Al sites in each material. Variable-temperature 27Al STMAS NMR studies of the two as-synthesized AlPO forms reveal the dynamics to be complex, with the motions of both the guest water molecules and organic template molecules shown to be contributing. The sensitivity of the STMAS NMR experiment to the presence of microsecond timescale dynamics is such that it seems likely that this methodology will prove useful in NMR studies of host-guest interactions in a wide variety of framework materials.