The Monte Carlo calculation of the effective (i.e. adjoint weighted) neutron generation time Λeff, especially for continuous energy simulations, is not straightforward nor standard in Monte Carlo codes. The use of the non-adjoint weighted neutron generation time Λ (standard in most Monte Carlo codes) as an approximation of the effective one can lead to a serious bias. We show here that the difference between Λeff and Λ can be more than 200% for a thermal fission system (VENUS reactor, SCK-CEN, Belgium) and more than 600% for a fast fission system (MASURCA reactor, Cadarache, France). For this, we have implemented, for the first time, in the Monte Carlo code MCNP(X), an asymptotically exact method for the calculation of Λeff. Our method was benchmarked against measurements in MASURCA: the difference between calculated and experimental values is less than 10%.