We propose a novel power efficient adaptive hybrid dynamic power management (AH-DPM) algorithm. To adapt well to bursty request arrival patterns with self-similarity and a service provider (SP, i.e., hard disk or WLAN NIC, in this paper) with multiple inactive states, the proposed AH-DPM first derives the average idle time of the SP in the bursty (ON) period and non-bursty (OFF) period separately. Then, to achieve better power saving, we use the average idle time in the ON period to adjust the timeout value more precisely and use the average idle time in the OFF period to decide which inactive state the SP should be switched to. Experimental results based on real traces show that, for the hard disk, the average power consumption of the proposed AH-DPM is better than that of the Adaptive Timeout (ATO), Machine Learning (ML), Predictive, Static Timeout (STO), and Stochastic algorithms. In addition, the average response time of the proposed AH-DPM algorithm is still lower than that specified in a typical hard disk specification. As to the WLAN NIC, experimental results show that the average power consumption of the proposed AH-DPM is comparable to that of the Oracle (theoretically optimal), ATO, and Predictive algorithms, and is better than that of the ML, STO, and Stochastic algorithms. However, the average packet transmission delay of the proposed AH-DPM is better than that of the ATO and Predictive algorithms. Therefore, by providing a better tradeoff between average power consumption and average response time (or average packet transmission delay), the proposed AH-DPM algorithm is very feasible for extending the battery lifetime of ever increasing mobile devices that are equipped with hard disks and WLAN NICs.