We consider how doping can be described in terms of the charge-transfe
r insulator concept. We discuss and compare a few models for the band
structure for the doped charges. This has led us to the conclusion tha
t the band structure stability problem is one of the main issues in an
y correspondence between results for the t-J model and, say, the three
-band model for the slightly doped layered oxides. The stability crite
rion is formulated and its implications discussed. Provided a phenomen
ological conduction band is chosen to satisfy the criterion of stabili
ty, a detailed picture of how dopants influence the spin wave spectrum
at T = 0 is presented. The basic physics for the destruction of the a
ntiferromagnetic (AF) long-range order is rather model-independent: th
e long-range order (at T = 0) disappears due to the Cerenkov effect wh
en the Fermi velocity first exceeds the spin wave velocity. We then di
scuss the overall spectrum of spin excitations and see that the spin w
ave attenuation for x < x(c), T = 0 due to Landau damping appears in t
he range of magnon momenta k(x) = 2ms +/- a square-root x. We also ar
gue that in the presence of superconductivity, the Cerenkov effect is
eliminated due to the gap in the spectrum. This may restore the role o
f the AF fluctuations as the main source of dissipation at the lowest
temperatures. A brief discussion of how interaction with magnons may a
ffect the hole spectrum concludes the paper.