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In this paper, we develop a resource allocation technique for a hybrid time division multiple access (TDMA) - non-orthogonal multiple access (NOMA) system with opportunistic time assignment. In particular, the available transmission time is divided into several time-slots, through which multiple users are served by exploiting power-domain NOMA. To fully exploit underlying benefits of this hybrid TDMA-NOMA system, we utilize the available resources efficiently by jointly allocating transmit power and time-slots to several groups of users in the system. Furthermore, these resources are allocated to maximize minimum rate of the users in the system. However, this max-min resource allocation problem is non-convex due to coupled design parameters of time and power allocations. Hence, we exploit a novel second-order cone formulation to overcome this non-convexity issue and develop an iterative algorithm to realize a solution to the original max-min problem. Simulation results show that this joint resource allocation technique has a considerable performance enhancement in terms of both minimum achieved rate and overall system throughput compared to that of the conventional resource allocation technique where equal time-slots are assigned to the groups of users.