How does this two opamp relaxation oscillator function?
1st: recognize these Op Amps and that the 1st is used as a unity DC gain with differentiator feedback on the output of the 2nd stage.
The 2nd stage  is used as a comparator looped back with positive feedback, but if has 0 input the output is 0.

2nd: recognise current limit of Op Amps and too low feedback R like 220 ohm may cause current limits. This design could easily be scaled by increasing all R's x 100 and reduce C by the same ratio /100 to get the same RC=T.

3rd: if the initial condition does not start a ramp voltage on the cap, it has nothing to differentiate.

Step 1: Assume all inputs and outputs are at 0V with Vcc,Vee=+5,-5V.
     U1 is scaled to 50% and so the R divider output (D) has an output of +/-2.5V with a source Req=1.1k

Step 2: Since the in+ ref= 0V the comparator output will amplify noise initially so the output of U1 may be high or low.  (contrary to your simulation, which has unknown or no noise)   

Step 3: If U2 is unity DC gain the output stays at 0V. what will U1 do? This looks like an integrator with high DC gain. But with negative feedback the integrator tends to correct itself and stay at zero unless there is an input offset voltage in the simulation.   Perhaps this is why it took a minute to finally oscillate.

Step 4: What happens at the input of U2?  When U1 out finally starts to ramp the input is attenuated at U2 by the feedback R 220 ohms with a source of Req=1.1k or about 8% of the output of U1. Since U1 has open loop gain, I am expecting the input to be microvolts and very slowing ramping with a slow but accelerating ramp.   


  This is getting tedius. It's a poor design with a split supply. It works best with a single supply with a split supply crossover threshold to start the ramp immediately.


The start up ramp relies on input offset voltage and a 1 minute start up ramp implies to me a 0 offset simulation.

If the Op Amps have no offset, then only simulator noise will eventually get enough picovolt error to slowly ramp. It's almost an ideal integrator until it accelerates with positive feedback to get into a realxtion mode with hystereis.


  The CMOS logic Schmitt Inverter works best with a single RC as a Relaxation oscillator for a general purpose RC clock.