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In this paper, we investigate the downlink performance of cell-free massive multi-input multi-output non-orthogonal mul-tiple access (CF-mMIMO-NOMA) system with conjugate beamforming precoder and compare against the orthogonal multiple ac-cess (OMA) counterpart. A novel achievable closed-form spectral efficiency (SE) expres-sion is derived, which characterizes the effects of the channel estimation error, pilot contami-nation, imperfect successive interference can-cellation (SIC) operation, and power optimiza-tion technique. Then, motivated by the closed-form result, a sum-SE maximization algorithm with the sequential convex approximation (SCA) is proposed, subject to each AP power constraint and SIC power constraint. Numer-ical experiments indicate that the proposed sum-SE maximization algorithms have a fast converge rate, within about five iterations. In addition, compared with the full power control (FPC) scheme, our algorithms can significant-ly improve the achievable sum-SE. Moreover, NOMA outperforms OMA in many respects in the presence of the proposed algorithms.