Two-dimensional weak-coupling Fröhlich polarons are investigated theoretically in the presence of an external magnetic field normal to the two-dimensional plane. For a weak magnetic field (cLO), the cyclotron mass approaches the zero-field polaron effective mass, whereas for large fields (cLO), the cyclotron mass approaches the bare band mass from below. In the resonance situation (cLO), the cyclotron mass shows an enhanced polaronic renormalization effect. Connection is made with recent data on magnetoabsorption in semiconductor space-charge layers, explaining why polaron effects show up only in some experiments. © 1984 The American Physical Society.