  We study the spaces of embeddings $S^m\hookrightarrow R^n$ and those of long
embeddings $R^m\hookrightarrow R^n$, i.e. embeddings of a fixed behavior
outside a compact set. More precisely we look at the homotopy fiber of the
inclusion of these spaces to the spaces of immersions. We find a natural fiber
sequence relating these spaces. We also compare the $L_\infty$-algebras of
diagrams that encode their rational homotopy type, when the codimension
$n-m\geq 3$.
