Jointly hyponormal pairs of commuting subnormal operators need not be   jointly subnormal
  We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of R. Curto, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality. 
Raul Curto and Jasang Yoon