Lecture materials from the Voroshilov Military Academy tell us that the Soviets usually used a three level alert system.

From "The Voroshilov Lectures" compiled by Ghulam Dastagir Wardak

There are three levels (stepen) of combat readiness (boevaia gotovnost):

• constant [or routine] (postoiannaia) combat readiness;

• increased (vysshaia) combat readiness;
• and full (polnaia) combat readiness.

You can refer to the source link to read up more on what exactly each of these readiness levels entailed. For the most part though, they match up with their names. Constant/routine readiness is just peacetime level actions. Increased readiness involves alerting the unit and recalling troops to bases to begin inspection and mobilization procedures. Full combat readiness is the unit basically ready to go to action.

In terms of nuclear situations, Bruce Blair's The Logic of Nuclear War expands on special orders outside of the three general levels:

If an enemy attack appeared imminent, Soviet forces could be raised to a state of utmost readiness as rapidly as possible by declaring a combat alert (boyevaya trevoga)...For the strategic nuclear forces, the notification by alert (opoveshcheniye po trevoge) brought them to full combat readiness in "only some minutes."

...The alert command that brought nuclear weapons and their operators to the brink of war was known to them as a preliminary (or sometimes a prepare) command (predavaritel'naya komanda).