The linearized response of a collisionless plasma model to external applied fields is calculated and examined with respect to its causal behavior. It is found that causality is not automatically fulfilled but must be imposed. The Titchmarsh theorem of complex analysis is used as a guide in imposing causality. Alternatively, it is shown that causality can be achieved by adding a damping term to the model and allowing the damping rate, which this term introduces, approach zero.