Given the dynamic changes in the regulatory environment, doing business in a global network (e.g. shipbuilding network) and the increasing use of voluntary certifications and standards, companies need effective tools to monitor and make continuous improvement. A maturity model for cruise shipbuilding network from a quality management and sustainability point of view is the focus of this article. Our research question is: What quality management maturity models, that take sustainability into account in supply network context, can be identified in the literature? This is work in progress as we are developing the maturity model structure searching performance theme areas and key performance indicators for the cruise ship building network. This article is based on a preliminary literature review with themes related to quality management and sustainability. Literature was collected from Scopus AI database in January 2025. The challenge is to develop a maturity model for the network context as the most of the articles are focused on one company maturity perspective.