  In a GaAs/AlGaAs quantum well of electron density 1x10^{11} cm^{-2} we
observe a fractional quantum Hall effect (FQHE) at filling factors nu=4/11, and
5/13, and weaker states at nu=6/17, 4/13, 5/17 and 7/11. These sequences of
fractions do not fit into the standard series of integral quantum Hall effects
(IQHE) of composite fermions (CF) at nu=p/(2mp +/- 1). They rather can be
regarded as the FQHE of CFs attesting to residual interactions between these
composite particles. In tilted magnetic fields the nu=4/11 state remains
unchanged, strongly suggesting it to be spin-polarized. The weak nu=7/11 state
vanishes quickly with tilt.
