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The time-dependent characteristics of a radio frequency superconducting quantum interference device (rf SQUID)involving two Josephson junctions connected in series are studied. First the dynamics of the total flux is given. Then the intrinsic flux noises in both nonhysteretic and hysteretic modes are investigated. The result shows that it is necessary to properly reduce the critical current ratio of the two junctions for low intrinsic noise level. When the critical current ratio is properly reduced, the intrinsic flux noise level of a two-junction rf SQUID is generally close to or slightly larger than that of a single junction rf SQUID, but no more than one order-of-magnitude.