In this paper we combine α stable noise with a monostable stochastic resonance (SR) system to investigate the overdamped monostable SR phenomenon with multiplicative and additive α stable noise, and explore the action laws of the stability index α (0 α ≤ 2) and skewness parameter β (-1 ≤ β ≤ 1) of the α stable noise, the monostable system parameter a, and the amplification factor D of the multiplicative α stable noise against the resonance output effect. Results show that for different distributions of α stable noise, the single or multiple low-and high-frequency weak signals detection can be realized by adjusting the parameter a or D within a certain range. For a or D, respectively, there is an optimal value which can make the system produce the best SR effect. Different α or β can regularly change the system resonance output effect. Moreover, when α or β is given different values, the evolution laws in the monostable SR system excited by low-and high-frequency weak signals are the same. The conclusions drawn for the study of single-and multi-frequency monostable SR with α stable noise are also the same. These results will be the foundation for realizing the adaptive parameter adjustment in the monostable SR system with α stable noise.