  We study the commutation relation for 2-radial SLE in the unit disc starting
from two boundary points. We follow the framework introduced by Dub\'{e}dat.
Under an additional requirement of the interchangeability of the two curves, we
classify all locally commuting 2-radial SLE$_\kappa$ for $\kappa\in (0,4]$: it
is either a two-sided radial SLE$_\kappa$ with spiral of constant spiraling
rate or a chordal SLE$_\kappa$ weighted by a power of the conformal radius of
its complement. Namely, for fixed $\kappa$ and starting points, we have exactly
two one-parameter continuous families of locally commuting 2-radial SLE.
Two-sided radial SLE with spiral is a generalization of two-sided radial SLE
(without spiral) which satisfies the resampling property. We define it by
weighting two independent radial SLEs by a two-time parameter martingale.
However, unlike in the chordal case, the resampling property does not uniquely
determine the pair due to the additional degree of freedom in the spiraling
rate. We also discuss the semiclassical limit of the commutation relation as
$\kappa \to 0$.
