In this paper we report on new RR Lyrae stars discovered in the first long run fields (LRc01 and LRa01) of the CoRoT mission. CoRoT frequency analysis of the high quality light curve with an unprecedented photometric accuracy and uninterrupted coverage over long period (∼150 days) are shown. The CoRoT results reveal four of the seven stars affected with the Blazhko effect and showing a very high fraction of the Blazhko stars ever obtained. The CoRoT RRLyrae stars show pulsation periods strongly nonlinear and complex multiplet structures, such as the triplet, quintuplet, septuplet, nonuplet, undecaplet, tredecaplet, quindecaplet and sepdecaplet frequency structures. Additional frequencies are detected as well with a linear combination with the fundamental radial mode, showing a strong evidence for direct detections of nonradial pulsations. We put into evidence new classes of RR Lyrae stars showing the Blazhko double mode RR Lyrae stars (fundamental and second overtone), nonradial and radial (multimodes) pulsations and new behaviour of the Blazhko effect, such as the Blazhko modulation in both mixing modes (second Blazhko effect), the CoRoT Blazhko results are consistent with Stothers'explanation of the Blazhko effect with period and amplitude changes. However, we stress for developing it in further theoretical investigation, with the aim of finding the physical mechanism behind the Blazhko enigma.