When presented with an oscillatory sensory input at a particular frequency, F [Hz], neural systems respond with the corresponding frequency, f [Hz], and its multiples. When the input includes two frequencies (F1 and F2) and they are nonlinearly integrated in the system, responses at intermodulation frequencies (i.e., n1*f1+n2*f2 [Hz], where n1 and n2 are non-zero integers) emerge. Utilizing these properties, the steady state evoked potential (SSEP) paradigm allows us to characterize linear and nonlinear neural computation performed in cortical neurocircuitry. Here, we analyzed the steady state evoked local field potentials (LFPs) recorded from the primary (S1) and secondary (S2) somatosensory cortex of anesthetized cats (maintained with alfaxalone) while we presented slow (F1 = 23Hz) and fast (F2 = 200Hz) somatosensory vibration to the contralateral paw pads and digits. Over 9 experimental sessions, we recorded LFPs from N = 1620 and N = 1008 bipolar-referenced sites in S1 and S2 using electrode arrays. Power spectral analyses revealed strong responses at 1) the fundamental (f1, f2), 2) its harmonic, 3) the intermodulation frequencies, and 4) broadband frequencies (50-150Hz). To compare the computational architecture in S1 and S2, we employed simple computational modeling. Our modeling results necessitate nonlinear computation to explain SSEP in S2 more than S1. Combined with our current analysis of LFPs, our paradigm offers a rare opportunity to constrain the computational architecture of hierarchical organization of S1 and S2 and to reveal how a large-scale SSEP can emerge from local neural population activities.