The fashion industry ranks among the most resource-intensive and environment-polluting industries. Circularity has been discussed as a solution to these problems. However, the transition towards a circular economy (CE) requires fundamental changes in the behavior and actions of all market entities. Consumer interest in sustainability and circularity can stimulate businesses to become more responsible and to offer circular solutions, and thus create a significant competitive advantage for these firms in a globalized market. This paper examines consumer attitudes towards the new circular models in the fashion industry (e.g. slow fashion, swapping, clothes rent, etc.). Consumer knowledge of these models, consumer willingness to support them as well as a correlation to selected demographic characteristics will be described along with consumer attitudes towards textile products made of waste and recycled material. Results will be introduced from a questionnaire survey carried out in October and November 2019 using the sample of 468 respondents in Slovakia. The obtained data were evaluated using statistical methods (Pearson Chi-Square, Wilcoxon test, Spearman’s correlation coefficient). While generally a low awareness of Slovak consumers of new models in the fashion industry was confirmed, the willingness of consumers to engage and support circular solutions was shown, especially among the younger generations. These results show that businesses that react to consumer expectations regarding circularity by offering products and services with environmental benefits may increase their competitiveness.