  In this paper we analyse time change equations (TCEs) for L\'evy-type
processes in detail. To this end we establish a connection between TCEs and
classical one-dimensional initial value problems (IVPs) which are easier to
handle. Properties of the IVPs are linked with properties of the TCEs. We show
in a general setting existence and uniqueness of solutions of the TCEs. Our
main result is based on the general path properties for L\'evy-type processes
found in Schnurr (2013). Applications include an existence result for processes
which correspond to a certain class of given symbols.
