OK, this looks like real data that possibly could be described by some simple theoretical model and you definitely don't need more than a handful of parameters once you have the right formula.
Is there some theory? What is the measurement?
Could you attach a file containing the raw data in five columns:
x, y(white), y(red), y(green), y(yellow)
and I'll try to play with it a bit.
Once you have a simple model, you just use the levenberg-Marquardt nlin fit to get the theoretical curves AND the interesting parameters. You definitely don't want a high-order polynominal fit or spline.