This article presents continuous-time (CT) analytical solutions to Hammerstein and Wiener systems with second-order plus-lead (SOPL) dynamic behavior for sinusoidal input changes. The proposed solutions depend only on the most recent input change and exact accuracy is demonstrated for cases of varying frequency (w), amplitude (A), and phase angle (gamma). This article demonstrates two critical advancements in the application of these solutions using a multiple input, multiple output (MIMO) mathematically simulated continuous stirred tank reactor (CSTR). The first one is improved accuracy over approximating periodic input changes as piece-wise step changes. The second one is the ability to accurately model process noise in the outputs when the input process noise can be decomposed into a sum of sinusoidal components. Since in many applications inputs are measured at a much higher rate than an output, the CT modeling of periodic process noise provides a means to model periodic output noise despite infrequent sampling of the output. Moreover, this article also presents output correction using measured output to remove prediction bias under white and serially correlated noise of measured outputs. (c) 2006 Elsevier Ltd. All rights reserved.