i dont know where the spikes appear , you can upload snapshot to clarify , but you may have two kinds of spike:
1- as output is zero except in one combination only, so spikes appear superimposed on the zero level, this cause of the rise & fall time of the two signals, you may notice that this spikes appears on transitions of inputs,and this might not cause a problem ,
2- spikes on while transition from zero to one i.e. the output comes to a higher level than Vdd (or the one level ), this also might not cause a problem as long as the spike value acceptable, it is in this case called overshoot, adding capacitances to the output may eliminate that but will increase your rise and fall time