In this paper, we first consider the Jacobsthal and Jacobsthal Lucas quaternions and octonions. By making use of definitions of these sequences, we derive some novel and interesting properties and relations for the Jacobsthal and Jacobsthal Lucas quaternions and octonions. As universal formulae for these sequences, we obtain the binet formulas. Finally, we introduce a new class of octonions of Jacobstal and Jacobstal Lucas sequences. We then investigate several new properties including Catalan identities, D'ocagene's identities and binet-like formulas.