Rami Arieli: " The Laser Adventure" Chapter 1.2.3 page 3
Example 1.3:

Can waves with different wavelength be coherent?

Solution to example 1.3:
Waves with different wavelengths can have the same phase in one point in space (or even in some points), but they can not keep this phase difference as can be seen in figure 1.10.

Figure 1-10: Waves with different wavelengths


As can be seen from this example, coherence depends on monochromaticity. Coherence is important for applications like interference and diffraction, and the entire process of holography is based upon it, as explained in chapter 10.