  The nature of $\kappa$-symmmetry transformations is examined for p-branes
embedded in a class of coset superspaces G/H, where G is an appropriate
supergroup and H is the Lorentz subgroup. It is shown that one of the
conditions $\delta Z^M E_M{}^a = 0$ which characterizes $\kappa$-symmetry
transformations arises very naturally if they are implemented in terms of a
right action of a subgroup of the supergroup G on the supergroup elements which
represent the coset. Unlike the global left action of G on G/H (which gives
rise to supersymmetry on the coset superspace), there is no canonically defined
right action of G on G/H. However, an interpretation of this right action
involving an enlargement of the isotropy group from the Lorentz subgroup to a
subgroup of G with generators which include some of the fermionic generators of
G is suggested. Closure of the generators of this larger subgroup under
commutation leads to the usual `brane scan' for p-branes which have bosonic
degrees of freedom which are worldvolume scalars.
