An iron-based rare earth alloy nanocomposite magnet has a composition represented by (Fe.sub.1-mT.sub.m).sub.100-x-y-zQ.sub.xR.sub.yTi.sub.z, where T is Co and/or Ni, Q is B and/or C and R is rare earth element(s) including substantially no La or Ce. x, y, z and m satisfy 10 at %