We study by extensive histogram Monte Carlo simulations the phase transition in the antiferromagnetic stacked triangular lattices with classical Heisenberg spins. It is shown that in a range of the antiferromagnetic next-nearest-neighbor interaction $J_2$, the transition is clearly of first order. We also reconsider the controversial question concerning the nature of the phase transition when $J_2=0$: we show that the critical exponents obtained, in agreement with previous simulations, exclude the possibility of the $O(4)$ class predicted by a nonlinear $\sigma$ model in $2+\epsilon$ renormalization-group calculation. The phase diagram in the ($J_2$,T) space (T: temperature) is shown and discussed. For comparison, the phase diagram obtained by a Green-function method in the case of {\it quantum} Heisenberg spins is also shown.[ps.gz] [ pdf]

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