The behaviour of the spherical derivative of meromorphic function with a Nevanlinna deficient value is studied. One of the results is the following Theorem 1. Let f be a transcendental meromorphic function satisfying conditions \[ \lim_{r\to \infty}(T(2r,f)/T(r,f)) = 1 \] and \(\delta (\infty,f)>0\). Then \[ \overline{\lim}_{r\to \infty}(r \sup \{| f'(z)| /(1+| f(z)|^ 2)|: | z| =r\}(T(r,f))^{-1}=\infty \] and \[ \overline{\lim}_{r\to \infty}n(r,0,f)\ell n(r \sup \{| f'(z)| /(1+| f(z)|^ 2): | z| =r\})(T(r,f))^{-1} \geq \delta(\infty,f). \]