Ethical nature of multiple post-doctoral applications I am a student applying in different places for postdoctoral positions and asking various faculties for position. It happened that, due to limited resources, I am not getting much response. However more than one faculty (from different institutes all in Europe) gave positive responses. The caveat is, I have to jointly write a research proposal with them for grant application/some fellowships. Whatever be the outcome of the proposal(s), I am starting my collaboration with them soon. 

My dilemma starts here. The fellowships each one suggested are very competitive. Those faculties themselves informed me that getting those fellowships became more difficult in the present financial situation. Now is it ethical to do apply for multiple funding agencies in this way? Fortunately, each of them suggested applying for different fellowships. I am slightly afraid of the morality of the whole issue (like: what if all of the projects get funding). Please help.
There is nothing wrong or strange to apply for several fellowships and funding as you describe. The opposite would mean you have to gamble on one and hope it comes through. What can be a bit problematic is perhaps if each proposal causes a lot of work for somebody in a department if you later is a no show despite funding. In such a case it would be good to let people know you are sending in other applications as well so they are not completely in the dark about your situation. I am sure everyone will be sympathetic. If they are not you may not want to go there anyway. 

The risk of getting money from several of your applications seems like a luxury problem. Yes, you have to decide which one to go for but that should be a pleasant problem. I would tackle the problem IF it becomes reality and not worry about it at this stage. Your first step is to get applications in, not worry about what to do when and if any funding comes through.