  We study the effect of Zeeman magnetic field in the superconducting phase
with two component order parameter scenario, such as, $d_{x^2-y^2} +
e^{i\theta}{\alpha}$, where $\alpha = d_{xy}, s$. This scenario is equivalent
to applying magnetic field parrllel to Cu-O planes. In a weak magnetic field,
which does not cause much change to the predominant d-wave, supresses the minor
$\alpha$ component leading to pure d-wave phase. This observation is in
contrary to the effect of magnetic field applied in the c-direction to the Cu-O
planes which is believed to induce a minor component $\alpha$ to d-wave
superconductors.
  We also show that the response of such superconductors to a weak Zeeman
magnetic field can be quite different depending on the phase $\theta$ of the
minor component ($\alpha$).
