  Thermodynamic stability of composite vortex in a two-component superconductor
is investigated by the Ginzburg-Landau theory. The predicted nature of these
vortices has recently attracted much attention. Here we consider axially
symmetric quantized vortex and show that the stability of vortex depends on
three independent dimensionless parameters: $\kappa _{1}$, $\kappa _{2}$,
$\kappa _{\xi}$, where $\kappa _{i}(i=1,2)$ is the Ginzburg-Landau parameter of
individual component, $\kappa _{\xi }=\xi _{1}/\xi _{2}$ is the ratio of two
coherence lengths. We also show that there exists thermodynamic stable vortex
in type-1+type-2 or type-2+type-2 materials over a range of these three
parameters.
