  Any ample Cartier divisor D on a projective variety X is strictly nef (i.e.
D.C>0 for any effective curve C on X). In general, the converse statement does
not hold. But this is conjectured to be true for anticanonical divisors.
  The present paper establishes this fact for normal complex projective
threefolds with canonical singularities. This result extends several previously
known special cases.
  The proof rests mainly on sophisticated techniques of three dimensional
birational geometry developed in the last two decades.
