Monte Carlo simulations, using the cooperative motion algorithm (CMA), have been employed to investigate the statics and dynamics of both symmetric and asymmetric diblock copolymer melts near the order-disorder transition. Investigation of the static properties has revealed the existence of two characteristic temperatures in the system: the ODT expressed as a peak in the heat capacity and a higher temperature T-1 at the crossover between the homogeneous state and the state with considerably increased concentration fluctuations. As T-1 is crossed, the increased amplitude of concentration fluctuations is accompanied by a significant increase of the average end-to-end distance of chains and the local chain orientation correlation. The dynamic properties of these systems have been observed by means of the relaxation of the single-bond, the chain end-to-end vector, and the block end-to-end vector, as well as by the single point concentration autocorrelation function. Corresponding relaxation times have been determined as a function of temperature. Below the ODT, a splitting of both the chain and the block end-to-end vector orientation correlation function is observed, while the relaxation of composition fluctuations becomes slower than that of the block orientation. The slow process is attributed to the conformal relaxation of the coherent interfaces formed in the ordered state.