In this paper, base on analysing the characters between the diode-pumped and krypton flashlamp-pumped lasers, we put forword a study of instability and chaos and of the elimination of chaos in krypton flashlamp-pumped intracavity frequency-doubled Nd:YAG lasers. Theoretical analyses and experimental apparatus are given, the results of chaotic laser radiation and its power spectra obtained through numerical calculation and experimental measurement are presented. By putting a Nd:YAG color center crystal in the resonator, the stable periodic laser radiation is attained and the elimination of chaos is realized.