  Let $f$ be an algebraically nondegenerate meromorphic mapping from $\mathbb
C^m$ into $\mathbb P^n(\mathbb C)$ and let $Q_1,...,Q_q$ be $q$ hypersurfaces
in $\mathbb P^n(\mathbb C)$ of degree $d_i$, in $N-$subgeneral position. In
this paper, we will prove that, for every $\epsilon >0$, there exists a
positive integer $M$ such that $$||\ (q-(N-n+1)(n+1)-\epsilon)
T_f(r)\le\sum_{i=1}^q\frac{1}{d_i}N^{[M]}(r,f^*Q_i)+o(T_f(r)).$$ Moreover, an
explicit estimate for $M$ is given. Our result is an extension of the previous
second main theorem for the mappings and moving hyperplanes or moving
hypersurfaces.
