Little research has been done on how the relationships of academic spin-off firms with their parent university influence their ability to attract funding for innovation activities. University is undoubtedly important for young spin-offs, not only because it provides knowledge and research facilities, but also because it enables access to financial capital. We drew on a sample of 100 firms in clarifying whether and how the relationship with the university increases the ability of the spin-offs in attracting funding for research and development and to what extent this depends on different network characteristics, such as size, density, strength of ties, and multiplexity. In this study we adopted the model of curvelinearity, derived from ideas on increasing and decreasing returns. We found that all four university network characteristics have a positive relationship with the spin-offs' ability to attract funding. Interestingly, diminishing returns were only identified when it comes to strength of ties and network multiplexity. Accordingly, a relationship tended to be beneficial as long as it was not too strong or too complex. Moreover, the ability to acquire funding tended to increase if the spin-offs develop a well-connected network of university and non-university contacts. The article concludes with some theoretical and practical implications and with suggestions for future research. (C) 2014 Elsevier Ltd. All rights reserved.