If you are in the process of doing something, you have begun and are continuing to do it. The administration is putting out a peace strategy. Her novel is currently being adapted into a television series. When you are on the process of doing something, you are still at the beginning of it and can stop at any time. The committee has not decided whether to approve the contract yet. They are on the process of deciding what role they will play in the recruitment campaign. Processes are methods or procedures used to accomplish goals. In this case, the process means that the administration is using different strategies to achieve its goal of bringing about peace between Israel and the Palestinians. The committee is still debating whether or not to approve the contract. It is also possible that they will reject it. You can also be in the process of doing something even though you are not at the beginning of it yet. She is still writing her book and it is not clear yet how it will end. However, she has already received an offer from a publisher so she must be close to finishing it. Being on the process of doing something is similar to being in the future. This statement means that even though the president has not done anything yet, he is already planning to bring about peace between Israel and Palestine.