The article examines the changes in the requirements for the development and implementation of innovations in the process of forming and improving supply chains in the face of increasing economic instability. Economic instability is presented as the most important trend in the modern economy and significant factor forming new requirements for supply chains. This, in turn, involves the improvement of applied technologies and development of new technologies, as well as the search for progressive technical and managerial solutions to meet the interests of a wide range of business entities and consumers of goods and services. A distinctive feature of this study is the fact that economic instability is viewed by the authors through the prism of both economic and non-economic processes having, inter alia, an impact on the economic system, including political, military, environmental, epidemiological and other processes. The article focuses on the COVID-19 coronavirus pandemic, as well as its impact on logistics solutions, and the specific demands on supply chains. It is substantiated that the introduction of technical and managerial innovations in this area will allow us to take into account the features and consequences of the impact of COVID-19 on the economy and to effectively influence the processes associated with improving supply chains. Thus, it will ensure compliance with the requirements and conditions determined by modern conditions associated with increased economic instability.