Sunspot penumbrae show a fine structure in continuum intensity that displays considerable dynamics . The magnetic field , in contrast , although also highly structured , has appeared to be relatively static . Here we report the discovery of inward moving magnetic enhancements in the penumbrae of two regular sunspots based on time series of SOHO/MDI magnetograms . Local enhancements of the LOS component of the magnetic field in the inner part of the penumbral region move inward to the umbra-penumbra boundary with a radial speed of about 0.3 km s ^ { -1 } . These local inward-moving enhancements of the LOS component of the magnetic fields appear to be relatively common . They are associated with dark structures and tend to display downflows relatively to the penumbral background . Possible explanations are discussed .