The astable multivibrator shown in above picture operates in a manner very similar to a free-running multivibrator using two cross-coupled NPN transistors.
Two NAND gates are used as linear amplifiers and their outputs are cross-coupled by capacitors C1 and C2. When the power is switched on, the output of one of the gates is slightly higher than the other because no two gates are exactly identical.
This difference is amplified and the positive feed-back provided by cross-coupling starts the oscillations. If the time constant R1, C1 and R2, C2 are equal, the output will be a symmetrical squarewave with equal on and off intervals.