  We have measured the transverse field muon spin precession in the flux
lattice (FL) state of the two gap superconductor MgB2 and of the electron doped
compounds Mg1-xAlxB2 in magnetic fields up to 2.8T. We show the effect of the
two gaps on the internal field distribution in the FL, from which we determine
two coherence length parameters and the doping dependence of the London
penetration depth. This is an independent determination of the complex vortex
structure already suggested by the STM observation of large vortices in a MgB2
single crystal. Our data agrees quantitatively with STM and we thus validate a
new phenomenological model for the internal fields.
