We have used the combined microwave spectroscopy: the nonresonant microwave absorption in low-magnetic field (so-called LFS) together with conventional ESR for the search and study of superconductivity (SC) in the new family of fullerene molecular solids: C60, C70, C76, C78, C84C90, and their alloys ((C60)1-y(C70)y), doped by different metals (K, Rb, In, and Ga) and iodine I2. These experiments fall into two categories: 1) Search for SC in higher fullerenes and study of the evolution of SC properties upon doping of pure (one component) fullerenes including Cm thin films. 2) Investigation of the Tcchange in molecular alloys of Mx(C60)1-y(C70)ytype. In the first category of experiments we discuss the evolution of LFS and ESR spectra upon variation of Rb-doping conditions: temperatures of doping: Td(C60), Td(M), and doping time td, and as a result we find the optimal conditions for vapour phase Rb-doping. Here we demonstrate that SC Tcappears and disappears with doping abruptly at a discrete value Tc28K for RbxC60similar to case of KxC60with a discrete Tc= 19K. It is shown that MxCn(n=70,76,78,84,90), InxC60, and GaxC60do not show SC phase at least at T>5K, while ESR changes dramatically upon doping. IxC60doped in ESR tubes at Td(C60,I2)=210° and 260°C also do not show LFS meaning absence of SC transition. However intensive ESR-signal appears proving the Occurrence of p-type charge transfer doping. In the second category we have found that Tcis strongly suppresed with increase ofyin molecular alloys of Kx(C60)1-y(C70)y, and in Rbx(C60)1-y(C70)y.