We have found nine burstlike events in EXOSAT data of the Z source Cyg X-2. Their durations are of the order of several seconds. Within the limited counting statistics we cannot find an indication for cooling during the burstlike events, which would have indicated that they are bona fide type I bursts, i.e., thermonuclear flashes on the surface of the neutron star. However, we find that typical X-ray burst properties (alpha, tau, gamma, fitted blackbody radii) hint at a type I burst origin. No evidence is found for coherent pulsations during the burstlike events. In order to determine the source state, i.e., to get an indication for the mass accretion rate, during the burstlike events, we studied the color-color diagrams during the corresponding observation periods. The burstlike events occurred in all branches in the X-ray color-color diagram, i.e., in the horizontal branch, the normal branch, and the flaring branch.