The existence of neutron stars with masses of \sim 2 M _ { \odot } requires a stiff equation of state at high densities .
On the other hand , the necessary appearance also at high densities of new degrees of freedom , such as hyperons and \Delta resonances , can lead to a strong softening of the equation of state with resulting maximum masses of \sim 1.5 M _ { \odot } and radii smaller than \sim 10 km .
Hints for the existence of compact stellar objects with very small radii have been found in recent statistical analysis of quiescent low-mass X-ray binaries in globular clusters .
We propose an interpretation of these two apparently contradicting measurements , large masses and small radii , in terms of two separate families of compact stars : hadronic stars , whose equation of state is soft , can be very compact , while quark stars , whose equation of state is stiff , can be very massive .
In this respect an early appearance of \Delta resonances is crucial to guarantee the stability of the branch of hadronic stars .
Our proposal could be tested by measurements of radii with an error of \sim 1 km , which is within reach of the planned LOFT satellite , and it would be further strengthened by the discovery of compact stars heavier than \sim 2 M _ { \odot } .