  The properties of the mass-radius curves of relativistic stellar models
constructed from an equation of state with a first-order phase transition are
examined. It is shown that the slope of the mass-radius curve is continuous
unless the discontinuity in the density at the phase transition point has a
certain special value. The curve has a cusp if the discontinuity is larger than
this value. The curvature of the mass-radius curve becomes singular at the
point where the high density phase material first appears. This singularity
makes the mass-radius curve appear on large scales to have a discontinuity in
its slope at this point, even though the slope is in fact continuous on
microscopic scales. Analytical formulae describing the behavior of these curves
are found for the simple case of models with two-zone uniform-density equations
of state.
