Systems are becoming more complicated, complex, and interrelated. Designers have recognized the need to develop systems from a holistic perspective and design them as Systems-of-Systems (SoS). The design of the SoS, especially in the conceptual design phase, is generally characterized by significant uncertainty. As a result, it is possible for all three types of uncertainty (aleatory, epistemic, and error) and the associated factors of uncertainty (randomness, sampling, confusion, conflict, inaccuracy, ambiguity, vagueness, coarseness, and simplification) to affect the design process. While there are a number of existing SoS design methods, several gaps have been identified: the ability to modeling all of the factors of uncertainty at varying levels of knowledge; the ability to consider both the pernicious and propitious aspects of uncertainty; and, the ability to determine the value of reducing the uncertainty in the design process.;While there are numerous uncertainty modeling theories, no one theory can effectively model every kind of uncertainty. This research presents a Hybrid Uncertainty Modeling Method (HUMM) that integrates techniques from the following theories: Probability Theory, Evidence Theory, Fuzzy Set Theory, and Info-Gap theory. The HUMM is capable of modeling all of the different factors of uncertainty and can model the uncertainty for multiple levels of knowledge.;In the design process, there are both pernicious and propitious characteristics associated with the uncertainty. Existing design methods typically focus on developing robust designs that are insensitive to the associated uncertainty. These methods do not capitalize on the possibility of maximizing the potential benefit associated with the uncertainty. This research demonstrates how these deficiencies can be overcome by identifying the most robust and opportunistic design.;In a design process it is possible that the most robust and opportunistic design will not be selected from the set of potential design alternatives due to the related uncertainty. This research presents a process called the Value of Reducing Uncertainty Method (VRUM) that can determine the value associated with reducing the uncertainty in the design problem before a final decision is made by utilizing two concepts: the Expected Value of Reducing Uncertainty (EVRU) and the Expected Cost to Reducing Uncertainty (ECRU). The techniques developed in this research, were combined into a robust and opportunistic design method specifically for the conceptual design of a SoS called CONceptual Design of Opportunistic and Robust System-of-Systems (CONDOR-SS). The utility of the individual techniques and the CONDOR-SS method as a whole are demonstrated through a number of example SoS design problems related to a persistent strike battlespace scenario.