The time-dependent surface coverage of antigen-antibody complexes for a sensor in which antigens are bound to surface immobilized antibodies is determined analytically. Assuming a reversible first order reaction between the antigens and antibodies, a model is derived describing the dynamical response of the sensor. The surface coverage is related explicitly to the antigen concentration which is of special interest in experimental situations. The stationary state and short time behaviour are determined explicitly. Several illustrations of the full solution are provided.