Title: Off Policy Average Reward Actor Critic with Deterministic Policy Search. Abstract: The average reward criterion is relatively less explored as most existing works in the Reinforcement Learning literature consider the discounted reward criterion. There are few recent works that present on-policy average reward actor-critic algorithms, but average reward off-policy actor-critic is relatively less explored. In this paper, we present both on-policy and off-policy deterministic policy gradient theorems for the average reward performance criterion. Using these theorems, we also present an Average Reward Off-Policy Deep Deterministic Policy Gradient (ARO-DDPG) Algorithm. We show a finite time analysis of the resulting three-timescale stochastic approximation scheme and obtain an $\epsilon$-optimal stationary policy with a sample complexity of $\Omega(\epsilon^{-2.5})$. We compare the average reward performance of our proposed algorithm and observe better empirical performance compared to state-of-the-art on-policy average reward actor-critic algorithms over MuJoCo based environments. 