There are two things coming into play here; the lamps and the dimmer(s).
First; LED and CFL type lamps that are to be used on a dimmer switch - must be identified for that use. Looks for the word dimmable
on the packaging or bulb itself. These lamps are generally a little more expensive than their non-dimmable counterparts. If it does not indicate it is dimmable, then it isn't - and should not be installed on a circuit controlled by a dimmer switch.
Second; a dimmer switch
that will be used to control LED and CFL bulbs (that are identified for use with a dimmer) must also be identified for use with dimmable LED and CFL bulbs. Again, these dimmer switches will be identified for this use and will cost more than those that work with standard filament type bulbs.
Lutron has dimmers for your circuit called a "C•L™ Dimmer" and supports Incandescent / Halogen, Dimmable Compact Fluorescent (CFL) and Dimmable Light Emitting Diodes (LED) type lamps. have a look here:
Lutron Maestro Dimmer and Switch Models
Also, be wary of the total load (wattage) of the lamps being controlled. If you have multiple dimmers in the same box, derating of the switch's wattage capacity (due to increased heat) will be required.