A possibility to accelerate a high intensity polarized proton beam up to 70 GeV at the IHEP accelerator, extract it from the main ring and deliver to several experimental setups is being studied now. We propose to study a wealth of single- and double-spin observables in various reactions using longitudinally and transverserly polarized proton beams at U70. The proposed measurements can be done at the existing detectors as well as require to create a few new experimental setups at U70.