In this paper, we introduce split dual Fibonacci and split dual Lucas octonions over the algebra $\widetilde{\stackrel{~}{O}}\left(a,b,c\right)$, where $a,b$ and $c$ are real numbers. We obtain Binet formulas for these octonions. Also, we give many identities and Vajda theorems for split dual Fibonacci and split dual Lucas octonions including Catalan's identity, Cassini's identity and d'Ocagne's identity.