what are the models original format? OBJ, X, 3DS, DAE? What are you using to convert? What options are you using when converting? Ive personally never seen anything like those pictures, but I have seen issues whenever the normals, binormals, and tangents were not being created during the conversion. The old converter for 3DWS would do this for any model that had more than texture applied. If you open up the model with the modelviewer, does each surface list normals, texcoords, binormals, tangents, and triangles? Also do you have anyway with your modeling program to check which direction the normals are facing?