Abstract The phenomenon of “J order” in scalar-coupled spin systems is discussed, analogies being drawn with states of dipolar and quadrupolar order. In particular the creation of a state of J order via the X region of an AX spin system by means of adiabatic demagnetization in the rotating frame (ADRF) is considered in detail. Equations are derived describing the ADRF process, as are equations describing the transfer of order from the J-ordered state to A-spin transverse magnetization in the presence of a resonant rf field near the A-spin Larmor frequency. Comparisons are made with pulse methods for producing the same J-ordered state and polarization transfer. The ability of ADRF to selectively produce a state of J order for a given value of the coupling constant J is considered and some pulse sequences are described briefly which are also capable of J-selective excitation of J-ordered states. Some possible general areas of application of these experiments are considered.