A multistage compressor is disclosed that may include a wobbling member operationally coupled with an external power source. The external power source may drive a nutating motion of the wobbling member. The multistage compressor may further include a plurality of flexible chambers connected to the wobbling member, each flexible chamber including a respective intake passage and a respective discharge passage. The wobbling member may sequentially press down and pull up the plurality of flexible chambers. The multistage compressor may further include a one-way valve in each respective intake passage and gas may be drawn into each flexible chamber through the respective one-way valve of each flexible chamber as the wobbling member pulls up each flexible chamber. The gas may then be compressed to a higher pressure as the wobbling member presses down each flexible chamber and compressed gas may be discharged through the respective discharge passage of each flexible chamber.