A compression system for an air conditioning system includes first and second compressors. The first compressor includes a first compression chamber in which a fluid introduced from an outside of the first compressor is compressed, and a first case defining a first space into which the fluid compressed in the first compression chamber is introduced. The second compressor includes a second case defining a second space into which the fluid compressed in the first compressor is introduced, and a second compression chamber in which the fluid introduced from the second space is compressed. The second compressor operates independently of the first compressor, and a connecting line connects the first and second compressors.