Context: Requirements Engineering (RE) has established itself as a software engineering discipline over the past decades. While researchers have been investigating the RE discipline with a plethora of empirical studies, attempts to systematically derive an empirical theory in context of the RE discipline have just recently been started. However, such a theory is needed if we are to define and motivate guidance in performing high quality RE research and practice. Objective: We aim at providing an empirical and externally valid foundation for a theory of RE practice, which helps software engineers establish effective and efficient RE processes in a problem-driven manner. Method: We designed a survey instrument and an engineer-focused theory that was first piloted in Germany and, after making substantial modifications, has now been replicated in 10 countries world-wide. We have a theory in the form of a set of propositions inferred from our experiences and available studies, as well as the results from our pilot study in Germany. We evaluate the propositions with bootstrapped confidence intervals and derive potential explanations for the propositions. Results: In this article, we report on the design of the family of surveys, its underlying theory, and the full results obtained from the replication studies conducted in 10 countries with participants from 228 organisations. Our results represent a substantial step forward towards developing an empirical theory of RE practice. The results reveal, for example, that there are no strong differences between organisations in different countries and regions, that interviews, facilitated meetings and prototyping are the most used elicitation techniques, that requirements are often documented textually, that traces between requirements and code or design documents are common, that requirements specifications themselves are rarely changed and that requirements engineering (process) improvement endeavours are mostly internally driven. Conclusion: Our study establishes a theory that can be used as starting point for many further studies for more detailed investigations. Practitioners can use the results as theory-supported guidance on selecting suitable RE methods and techniques.