  We classify quasilinear systems in Riemann invariants whose characteristic
webs are linearizable on every solution. Although the linearizability of an
individual web is a rather nontrivial differential constraint, the requirement
of linearizability of characteristic webs on all solutions imposes simple
second-order constraints for the characteristic speeds of the system. It is
demonstrated that every such system with n>3 components can be transformed by a
reciprocal transformation to n uncoupled Hopf equations. All our considerations
are local.
