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We consider resonances associated to the operator $-\frac{d^2}{dx^2}+V(x)$,where $V(x)=V_+$ if $x>x_M$ and $V(x)=V_-$ if $x<-x_M$, with $V_+\not = V_-$.We obtain asymptotics of the resonance-counting function in several regions.Moreover, we show that in several situations, the resonances, $V_+$, and $V_-$determine $V$ uniquely up to translation.

Resonances for steplike potentials: Forward and inverse results