The critical dynamics of 'model A" of Hohenberg and Halperin has been studied by the Monte Carlo method. Simulations have been carried out in the three-dimensional (3d) simple cubic Ising model for lattices of sizes L = 16 to L = 512. Using Wolff's cluster algorithm, the critical temperature is precisely found as β c = 0.221 654 68(5). By Fourier transform of the lattice configurations, the critical scattering intensities I (q) can be obtained. After circular averaging, the static simulations with L = 256 and L = 512 provide an estimate of the critical exponent γ /ν = 2 − η = 1.9640(5). The | q |-dependent distribution of I (q) showed an exponential distribution, corresponding to a Gaussian distribution of the scattering amplitudes for a large q domain. The time-dependent intensities were then used for the study of the critical dynamics of 3d lattices at the critical point. To simulate results of an x-ray photon correlation spectroscopy experiment, the time-dependent correlation function of the intensities was studied for each | q |-value. In the q region where I (q) had an exponential distribution, the time correlations can be fit to a stretched exponential, where the exponent μ = γ /νz 0.975 provides an estimate of the dynamic exponent z. This corresponds to z = 2.0145, in agreement with the observed variations of the characteristic fluctuation time of the intensity: τ (q) ∝ q −z , which gives z = 2.015. These results agree with the expansion of field-theoretical methods (2.017). In this paper, the need to take account of the anomalous time behavior (μ < 1) in the dynamics is exemplified. This dynamics reflects a nonlinear time behavior of model A, and its large time extension is discussed in detail.