This two-part paper addresses characteristic properties of time-critical software-intensive systems (e.g. embedded, real-time, remote monitoring and diagnosis systems). These properties lie in the interface between systems engineering and software engineering. The first part of the paper pinpoints existing problems, the second one discusses potential resolution routes. The first part starts from observations of the current systems development process with the focus on stages for specification of requirements and design. The key problem, in addition to the increase of the overall complexity of systems, is the increasing role of emergent (e.g. non-predictable) system behaviour, its causes and methods for maintaining better control over the system emergent behaviour.