The theory of inelastic electron resonant tunneling through a double-barrier nanostructure is extended to establish a theory of phonon-assisted resonant magnetotunneling when a magnetic field is applied parallel to the tunneling current. At higher temperatures we have discovered an interesting characteristic oscillation of the width and height of the main peak in the I-Y curve when the ratio ω 0 /ω c changes between integer (double resonant) and half integer (single resonant), where ω 0 is the LO phonon frequency and ω c is the cyclotron frequency in the well. If confirmed experimentally, our theoretical prediction provides an additional method to determine the electronic effective mass in the well