  We study a nonlinear development of radial pulsation instability to a
resonant excitation of nonradial modes. Our theory covers the cases of
axisymmetric (m=0) modes as well as (m,-m) pairs. Adopting a simplified
treatment of the radial and nonradial mode coupling we find that the asymptotic
state is a pulsation with constant amplitudes and we evaluate the relative
amplitude of the nonradial component.
  Observable consequence of the m=0 mode excitation is a small period change
and a more significant amplitude change, especially in the case of a dipole
mode (l=1). Such a mode has a fairly large excitation probability.
  Significant amplitude and phase modulation is predicted in the case of
excitation of a m=1,-1 pair. We suggest that this may explain Blazhko-type
modulation in RR Lyr stars. If this model is correct, the modulation period is
determined by the rotation rate and the Brunt-Vaisala frequency in the deepest
part of the radiative interior.
