Epoxy resin-based fibre matrix compositions contain alkyl substituted ethylene amines such as dimethyldiethylenetriamine (DMDETA, also dimethyl-1,4,7-triazaheptane), as a curing agent. These curing agents are characterized by a short curing time for a comparatively long processing time, and make it possible to obtain cured epoxy resins that exhibit low brittleness and high tensile strength and have a high glass transition temperature; as a result of which the fibre matrix composition is suitable particularly for use in pultrusion and winding processes.