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We employ magnetocapacitance measurements to study the spectrum of a doublelayer system with gate-voltage-tuned electron density distributions in tiltedmagnetic fields. For the dissipative state in normal magnetic fields at fillingfactor $\nu=3$ and 4, a parallel magnetic field component is found to give riseto opening a gap at the Fermi level. We account for the effect in terms ofparallel-field-caused orthogonality breaking of the Landau wave functions withdifferent quantum numbers for two subbands.Comment: 4 pages, 4 figures included, to appear in JETP Letter

Opening an energy gap in an electron double layer system at the integer filling factor in a tilted magnetic field