In an ideal world, with ideal capacitors, one will be enough. But the real capacitors have also a series inductance, due to its package, terminals, construction, etc. One important parameter of a capacitor is the SRF (series resonant frequency) and usually it can be found in the datasheet. The capacitor acts as a capacitor at working frequencies below its characteristic SRF, but after that, it begins to act like an inductor. Usually, capacitors with higher values have lower characteristic SRF. The power supply filter from the image has two capacitors because it probably must filter a wide range of noise induced in the power supply lines by the opamp. The 1uF capacitor will filter the low spectral components, but due to its low SRF, it is useless at higher frequencies. Here comes into place the 0,1uF capacitor, which is more efficient at higher frequencies, due to its higher SRF, but this one is useless at lower frequencies. It is not uncommon to see for example in very high speed digital circuits more than two capacitors at the power supply line (100pF, 1nF, 10nF...etc), exactely for this reason.
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Here you will find a nice program which will show you the behaviour of a capacitor, you will see its SRF, ESR, impedance at various freq. etc., for a wide range of capacitors, in various packages, materials, types, etc. Remember that the values are for their components, other manufacturers will have other parameters.
/pisoiu