The 30 and 44 GHz Back End Modules (BEM) for the Planck Low Frequency Instrument are broadband receivers (20% relative bandwidth) working at room temperature. The signals coming from the Front End Module are amplified, band pass filtered and finally converted to DC by a detector diode. Each receiver has two identical branches following the differential scheme of the Planck radiometers. The BEM design is based on MMIC Low Noise Amplifiers using GaAs P-HEMT devices, microstrip filters and Schottky diode detectors. Their manufacturing development has included elegant breadboard prototypes and finally qualification and flight model units. Electrical, mechanical and environmental tests were carried out for the characterization and verification of the manufactured BEMs. A description of the 30 and 44 GHz Back End Modules of Planck-LFI radiometers is given, with details of the tests done to determine their electrical and environmental performances. The electrical performances of the 30 and 44 GHz Back End Modules: frequency response, effective bandwidth, equivalent noise temperature, 1/f noise and linearity are presented.