  In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional
sigma models on special holonomy manifolds have extra symmetries that are in
one-to-one correspondence with the covariantly constant forms on these
manifolds. The superconformal algebras extended by these symmetries close as
W-algebras, i.e. they have field-dependent structure functions. It is shown
that it is not possible to write down cohomological equations for potential
quantum anomalies when the structure functions are field-dependent. In order to
do this it is necessary to linearise the algebras by treating composite
currents as generators of additional symmetries. It is shown that all cases can
be linearised in a finite number of steps, except for G_2 and SU(3). Additional
problems in the quantisation procedure are briefly discussed.
