We present observations with the new 11 GHz radiometer of the COSMOSOMAS experiment at the Teide Observatory ( Tenerife ) . The sky region between 0 ^ { \circ } \leq RA \leq 360 ^ { \circ } and 26 ^ { \circ } \leq DEC \leq 49 ^ { \circ } ( ca . 6500 square degrees ) was observed with an angular resolution of 0.9 ^ { \circ } . Two orthogonal independent channels in the receiving system measured total power signals from linear polarizations with a 2 GHz bandwidth . Maps with an average sensitivity of 50 \mu K per beam have been obtained for each channel . At high Galactic latitude ( |b| > 30 ^ { \circ } ) the 11 GHz data are found to contain the expected cosmic microwave background as well as extragalactic radiosources , galactic synchrotron and free-free emission , and a dust-correlated component which is very likely of galactic origin . At the angular scales allowed by the window function of the experiment , the dust-correlated component presents an amplitude \Delta T \sim 9–13 \mu K while the CMB signal is of order 27 \mu K. The spectral behaviour of the dust-correlated signal is examined in the light of previous COSMOSOMAS data at 13-17 GHz and WMAP data at 22-94 GHz in the same sky region . We detect a flattening in the spectral index of this signal below 20 GHz which rules out synchrotron radiation as being responsible for the emission . This anomalous dust emission can be described by a combination of free-free emission and spinning dust models with a flux density peaking around 20 GHz .