  We study the energetics of superconducting vortices in the SO(5) model for
high-$T_c$ materials proposed by Zhang. We show that for a wide range of
parameters normally corresponding to type II superconductivity, the free energy
per unit flux $\FF(m)$ of a vortex with $m$ flux quanta is a decreasing
function of $m$, provided the doping is close to its critical value. This
implies that the Abrikosov lattice is unstable, a behaviour typical of type I
superconductors. For dopings far from the critical value, $\FF(m)$ can become
very flat, indicating a less rigid vortex lattice, which would melt at a lower
temperature than expected for a BCS superconductor.
