We consider Josephson vortices at tricrystal boundaries. We discuss the specific case of a tricrystal boundary with a pi junction as one of the three arms. It is recently shown that the static system admits an (n+1/2) phi₀ flux, n=0,1,2 [Phys. Rev. B 61, 9122 (2000)]. Here we present an analysis to calculate the linear stability of the admitted states. In particular, we calculate the stability of a 3 phi₀/2 flux. This state is of interest, since energetically this state is preferable for some combinations of Josephson lengths, but we show that in general it is linearly unstable. Finally, we propose a system that can have a stable (n+1/2)phi₀ state.