Enterprise information systems are increasingly being developed as distributed information systems. Quality attributes of distributed information systems, as in the centralised case, should be evaluated as early and as accurately as possible in the software engineering process. In particular, software measures associated with quality attributes of such systems should consider the characteristics of modern distributed technologies. Early design decisions have a deep impact on the implementation of distributed enterprise information systems and thus, on the ultimate quality of the software as an operational entity. Due to the fact that the distributed-software engineering process affords software engineers a number of design alternatives, it is important to develop tools and guidelines that can be used to assess and compare design artefacts quantitatively. This dissertation makes a contribution to the field of Software Engineering by proposing and evaluating software design measures for distributed enterprise information systems. In previous research, measures developed for distributed software have been focused in code attributes, and thus, only provide feedback towards the end of the software engineering process. In contrast, this thesis proposes a number of specific design measures that provide quantitative information before the implementation. These measures capture attributes of the structure and behaviour of distributed information systems that are deemed important to assess their quality attributes, based on the analysis of the problem domain. The measures were evaluated theoretically and empirically as part of a well defined methodology. On the one hand, we have followed a formal framework based on the theory of measurement, in order to carry out the theoretical validation of the proposed measures. On the other hand, the suitability of the measures, to be used as indicators of quality attributes, was evaluated empirically with a robust statistical technique for exploratory research. The data sets analysed were gathered after running several experiments and replications with a distributed enterprise information system. The results of the empirical evaluation show that most of the proposed measures are correlated to the quality attributes of interest, and that most of these measures may be used, individually or in combination, for the estimation of these quality attributes-namely efficiency, reliability and maintainability. The design of a distributed information system is modelled as a combination of its structure, which reflects static characteristics, and its behaviour, which captures complementary dynamic aspects. The behavioural measures showed slightly better individual and combined results than the structural measures in the experimentation. This was in line with our expectations, since the measures were evaluated as indicators of non-functional quality attributes of the operational system. On the other hand, the structural measures provide useful feedback that is available earlier in the software engineering process. Finally, we developed a prototype application to collect the proposed measures automatically and examined typical real-world scenarios where the measures may be used to make design decisions as part of the software engineering process.