In this letter, we analyze the performance of cognitive amplify-and-forward multirelay networks with active direct link in the presence of relay transceiver hardware impairments. Considering distortion noises on both interference and main data links, we derive tight closed-form outage probability expressions and their asymptotic behavior for partial relay selection (PRS) and opportunistic relay selection (ORS) schemes over Rayleigh fading channels. Both PRS and ORS schemes are found to attain full diversity for low target rates only, otherwise a relay cooperation ceiling (RCC) phenomenon occurs. We further illustrate that a perfect direct link can partially compensate for this RCC effect over high data rates for the two considered schemes. Numerical and simulation results validate our theoretical analysis.