The growing interest in the field of negative Poisson's ratio materials is motivated by the attractive mechanical properties of these materials and the potential enhancements that might be derived from replacing a positive Poisson's ratio component with its auxetic counterpart. In this paper we report on preliminary results of an ongoing experimental study to test the hypothesis that an auxetic composite can be produced by embedding an auxetic fibre network within a conventional (positive Poisson's ratio) matrix. First we present results of tensile tests performed on samples of compressed mats of sintered stainless steel fibres which are known to have a negative Poisson's ratio out-of-plane. Next we present results of mechanical tests and imaging studies on composite samples made by infusing the stainless steel mats with a polymer. Finally we report on the auxetic behaviour observed in some polymer nanocomposites with a high loading of carbon nanofibers. We conjecture that the embedded nanofibers form an effective network and, like the stainless steel mats, the compression of the samples during fabrication renders the embedded networks auxetic. The compliance of the polymer matrix relative to the nanofiber network results in an auxetic composite. The results demonstrate the feasibility of the approach and the potential for developing new auxetic composites with auxetic fibre networks as the reinforcing phase.