  When a magnetic field is applied along a direction deviated from the
quantization $Z$-axis, the conservation of total magnetization holds no more.
In this case the inclined field can cause a strong spin-evolution via the
linear Zeeman term even the field is as weak as a percentage of $mG$. An
approach beyond the mean field theory is proposed to study the evolution of
small $^{87}$Rb condensates under the weak inclined fields. The time-dependent
populations of spin-components are given in analytical forms. The evolution is
found to be highly sensitive to the magnitude and direction of the field.
