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A systematic analysis of the Burgers\u2013Kardar-Parisi-Zhang equation in d+1 dimensions by dynamic renormalization-group theory is described. The fixed points and exponents are calculated to two-loop order. We use the dimensional regularization scheme, carefully keeping the full d dependence originating from the angular parts of the loop integrals. For dimensions less than dc=2 we find a strong-coupling fixed point, which diverges at d=2, indicating that there is nonperturbative strong-coupling behavior for all d\u22652. At d=1 our method yields the identical fixed point as in the one-loop approximation, and the two-loop contributions to the scaling functions are nonsingular. For d>2 dimensions, there is no finite strong-coupling fixed point. In the framework of a 2+\u03b5 expansion, we find the dynamic exponent corresponding to the unstable fixed point, which described the nonequilibrium roughening transition, to be z=2+O(\u03b53), in agreement with a recent scaling argument by Doty and Kosterlitz [Phys. Rev. Lett. 69, 1979 (1992)]. Similarly, our result for the correlation length exponent at the transition is 1/\u03bd=\u03b5+O(\u03b53). For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.