Very first values of y[n] in an IIR filter I use a simple biquad IIR filter  :

if (n &gt;= 2)
   y[n] = (b0/a0)*x[n] + (b1/a0)*x[n-1] + (b2/a0)*x[n-2]
                    - (a1/a0)*y[n-1] - (a2/a0)*y[n-2] 
else
   y[n] = x[n]     // here it probably needs to be modified


(thanks to http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt)

It works very well.

My problem is that the filtered signal sometimes explodes in the first milliseconds, and then returns to normal after a few milliseconds.

How should I initiallize the first values of y[n] ? I have done this

y[n] = x[n]


for n=0,1, but probably the problem comes from here ?

The problem (it explodes in the first milliseconds) is important when I do 2, 3, or more passes of the same filter in cascade.

Thanks in advance.
Typically, you would initialize the filter state (which in your example includes $x[-1]$, $x[-2]$, $y[-1]$, and $y[-2]$) with zeros. This is equivalent to assuming that the filter is causal.