  The factorization problem of the multi-component 2D Toda hierarchy is used to
analyze the dispersionless limit of this hierarchy. A dispersive version of the
Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators
is introduced and the corresponding additional symmetries and string equations
are discussed. Then, it is shown how KP and Toda pictures of the dispersionless
Whitham hierarchy emerge in the dispersionless limit. Moreover, the additional
symmetries and string equations for the dispersive Whitham hierarchy are
studied in this limit.
