  We formulate a strong-coupling theory for perpendicular standing spin waves
(PSSWs) in ferromagnetic bilayers with the interlayer exchange coupling (IEC).
Employing the Hoffmann boundary condition and the energy-flow continuity across
the interface, we show that the PSSWs are still quantized but with non-integral
quantum numbers, in sharp contrast to that of a single layer. The magnon-magnon
coupling is characterized by the spectrum splitting which is linear with the
IEC in the weak-coupling region, but getting saturated in the strong-coupling
limit. Analytical predictions are verified by full micromagnetic simulations
with good agreement.
