  Structured stochastic processes evolving in continuous time present a widely
adopted framework to model phenomena occurring in nature and engineering.
However, such models are often chosen to satisfy the Markov property to
maintain tractability. One of the more popular of such memoryless models are
Continuous Time Bayesian Networks (CTBNs). In this work, we lift its
restriction to exponential survival times to arbitrary distributions. Current
extensions achieve this via auxiliary states, which hinder tractability. To
avoid that, we introduce a set of node-wise clocks to construct a collection of
graph-coupled semi-Markov chains. We provide algorithms for parameter and
structure inference, which make use of local dependencies and conduct
experiments on synthetic data and a data-set generated through a benchmark tool
for gene regulatory networks. In doing so, we point out advantages compared to
current CTBN extensions.
