Why won't my drivers side blinker work with head lights on?

Recently I have noticed that my
driver's side blinker (front and rear)
will not work when my head lights
are on. The bulbs light up, but will
not flash. When my head lights are
off, both front and rear blinkers work
as they should. I checked both bulbs
and filaments appear to be intact. I
replaced the rear bulb anyway, as it
appeared to have a burn mark on it,
and still nothing. I also looked at the
sockets, and they appear to be in
good shape. Could it be the flasher?
Or would a bad flasher cause both
blinkers to not work? Not sure what
else I could check.