Where did you get the textures? Normal maps can be a little complicated. There are a number of types (Object, World, Tangent) and different formats (all the check boxes in the Normals Channel). Generally speaking you need a tangent-type map of your object is going to be deforming.
From the help file:
The following rule of thumb applies to the most common method, Tangent:
• If the Normal texture is mostly light green, activate Swap Y & Z (Y up).
• If the Normal texture is mostly light blue, deactivate Swap Y & Z (Y up).