Translations for illegally in French

Here are paragraphs from public domain books translated:
"If I am Mr. Neville St. Clair, then it is obvious that no crime has been committed, and that, therefore, I am illegally detained." — Si je suis bien M. Neville Saint-Clair, il est alors évident qu’il n’y a pas crime et que je suis illégalement détenu.
The Adventures of Sherlock Holmes, by Arthur Conan Doyle Les Aventures de Sherlock Holmes, de Arthur Conan Doyle