Blend rules for (a) homogeneous and (b) heterogeneous systems are proposed in a form Of P = (phi1(m)P1 + phi2(m)P2)/(phi1m + phi2m), where P is the property, and phi, the volume fraction of component 1 or 2. For (a) m > 1 and for P2 > P1, an S-shaped relation occurs between P or phi1. On the contrary, for (b) m < 1, an anti-S-shaped relation occurs. When the hard component forms particles in continuous soft media, P is larger than the arithmetic mean PBAR. When the interface slips, a mean of harmonic function holds so that 1/P = phi1/P1 + phi2/P2 and P < PBAR. For special cases, i.e., the filler in the rubber and the rubber particles in the resin, the strength at break attains a maximum at 20 and 13% of particles, respectively. For rubber blended with a small amount of polypropylene by dynamic vulcanization, the latter forms a continuous phase, reinforcing rubber domains by the plastic force when the size of rubber particles becomes very small. 1994 John Wiley & Sons, Inc.