The evolution of the emission spectrum of an active nucleus during an individual active event is considered. The following assumptions are made: 1) the distribution of the line-emitting clouds in the region of formation of the broad lines is isotropic with respect to the ionizing source; 2) a typical cloud radiates in the lines primarily in the direction turned toward the source; 3) the luminosity of a typical cloud in a line is proportional to the power s of the ionizing flux incident on it (L ..cap alpha.. F/sup s/, where the value of s depends on the choice of the line). Expressions are obtained for the dependences ..delta..A(s) and ..delta..A(..delta..t), where ..delta..A is the maximal relative increment of the flux in the line (the amplitude), and ..delta..t is the time of delay of the maximum of the outburst in the line relative to the maximum of the outburst in the ionizing continuum. The dependences are compared with published date on the spectral variability of the Seyfert galaxy NGC 4151. It is concluded, in particular, that both the duration and amplitude of a typical outburst of NGC 4151 in the unobserved ionizing continuum is appreciably greater (possibly by an ordermore » of magnitude) than in the observed x rays.« less