This paper presents a Bayesian approach to the problem of searching for multiple lost targets in a dynamic environment by a team of autonomous sensor platforms. The probability density function (PDF) for each individual target location is accurately maintained by an independent instance of a general Bayesian filter. The team utility for the search vehicles trajectories is given by the sum of the `cumulative' probability of detection for each target. A dual-objective switching function is also introduced to direct the search towards the mode of the nearest target PDF when the utility becomes too low in a region to distinguish between trajectories. Simulation results for both clustered and isolated targets demonstrate the effectiveness of the proposed search strategy for multiple targets.