A process for producing a crosslinkable silyl group-containing polymer which
is
excellent in oil resistance, heat resistance, weatherability, low staining properties,
and compression set characteristics, includes the steps of radically polymerizing
a vinyl monomer in the presence of a thiocarbonylthio group-containing compound
with a specific structure, and introducing crosslinkable silyl groups. Also provided
is a curable composition which contains the polymer and which is easy to handle.