  We calculate the quantum phase diagram of the {\it XXZ} chain with
nearest-neighbor (NN) $J_{1}$ and next-NN exchange $J_{2}$ with anisotropies
$\Delta_{1}$ and $\Delta_{2}$ respectively. In particular we consider the case
$\Delta_{1}=-\Delta_{2}$ to interpolate between the {\it XX} chain ($%
\Delta_{i}=0$) and the isotropic model with ferromagnetic $J_{2}$. For $%
\Delta_{1}<-1$, a ferromagnetic and two antiferromagnetic phases exist. For $|
\Delta_{i}| <1$, the boundary between the dimer and spin fluid phases is
determined by the method of crossing of excitation spectra. For large
$J_{2}/J_{1}$, this method seems to indicate the existence of a second spin
fluid critical phase. However, an analysis of the spin stiffness and magnetic
susceptibility for $\Delta_{1}=\Delta_{2}=1$ suggest that a small gap is
present.
