We report on the magnetic properties of a Ni(2+)-vermiculite intercalation compound from Santa Olalla, Huelva (Spain). This modified vermiculite was studied by means of DC and AC magnetic measurements. The existence of two maxima in magnetic susceptibility below 10 K was interpreted in terms of the Cole-Cole formalism as being due to spin-glass freezing in this material. The temperature, frequency and external magnetic field dependences of these anomalies located at temperatures around 2-3 K and 8-10 K in the imaginary part of the magnetic susceptibility, χ″, seem to suggest the existence of spin-relaxation phenomena between the magnetic moments of the Ni(2+) ions. A dynamic study of the relaxation processes associated with these phenomena considering the Cole-Cole formalism allows us to interpret the anomaly found at 2-3 K according to a law of activated dynamics, obtaining values for the critical exponent, ψν < 1, characteristic of a d = 2 spin-glass-like system, while the maximum observed in χ″ at 8-10 K can be described by means of a law of standard dynamics with a value of the exponent z of around 5, representative of a d = 3 spin-glass-like system.