Electronic – MOSFET oscillation with gate resistance

I'm trying to make a current buffer for high currents, using an LM324 and BUZ70. This is the circuit:

^{simulate this circuit – Schematic created using CircuitLab}

I've noticed that this circuit starts to have a little oscillation (at least 100 times more the Vs frequency) overlapped to the gate voltage if a gate resistance of around 10Kohm is used. Removing this resistance, will remove the oscillation.

Just for completeness, there is also an evident miller effect, in which the initial ramp before the miller plateau is enlarged if a gate resistor of 10K is used, and this should be coherent.

The oscillation disappears also if the led is fed at 5V.

If Vs is a DC voltage, the oscillation takes place too, showing that it is NOT a transient ringing.

It is a breadboarded circuit, but in any case, I think that I have a very little phase margin, but this circuits should have a very large bandwidth.

Any opinion?

edit: when the LED is turned on, fraction of this oscillation is present in V_Power. I may solve this by putting a cap here and there and not using an high gate resistance, but I'd prefer to understand why, if it is possible.

edit1: as stated in comments, I need a compesation if the source resistance is less than 50 ohm. I don't understand, because modelling the system using this circuit:

^{simulate this circuit}

I obtain

$$V_{out}= \frac{R_s G_m}{1+R_s G_m} \frac{1-\frac{s}{z_1}}{1-\frac{s}{p_1}} V_{oa} = k V_{oa}$$

with $$z_{1} = -\frac{g_m}{C_{gs}}$$ $$p_{1} = -\frac{1}{C_{gs}\frac{R_s}{1+g_m R_s}}$$

and this does not affect the stability of the opamp, which is an LM324 with a limited band. The Cgs used is the provided Ciss, the gm = 2 (because of the limited current used now, see datasheet of BUZ70).

In fact, this MOSFET stage have the Vout/Voa with a bode of:

Therefore I can consider the system with the OPAMP asa voltage follower. Why I need to add compensation with low Rs values?