Predictive fetching and decoding for selected instructions (e.g., operating system instructions, hypervisor instructions or other such instructions). A determination is made that a selected instruction, such as a system call instruction, an asynchronous interrupt, a return from system call instruction or return from asynchronous interrupt, is to be executed. Based on determining that such an instruction is to be executed, a predicted address is determined for the selected instruction, which is the address to which processing transfers in order to provide the requested services. Then, fetching of instructions beginning at the predicted address prior to execution of the selected instruction is commenced. Further, speculative state relating to a selected instruction, including, for instance, an indication of the privilege level of the selected instruction or instructions executed on behalf of the selected instruction, is predicted and maintained.