The dynamics of shear Alfvenic disturbances in the vicinity of two-dim
ensional magnetic null X-points is studied. The study complements rece
nt work on compressional Alfvenic disturbances near X-points. For dist
urbances not straddling the separatrix, it is found that the shear Alf
ven wave phase mixes rapidly. The damping rate, however, is not as lar
ge as [ln(1/eta)](-2), as was found for magnetosonic disturbances (eta
is the resistivity). For low-frequency forced motions straddling the
separatrix, sheet currents are formed at the separatrix and the curren
t layer width is found to scale as eta(1/2). This results in a volumet
ric ohmic heating rate which also scales as eta(1/2).