Assuming that <math>\mathcal{S} = \mathcal{T}</math>, another model, known as the functional concurrent model, sometimes also referred to as the varying-coefficient model, is of the form
where <math>\alpha_0</math> and <math>\alpha</math> are coefficient functions. Note that model ({{EquationNote|6}}) assumes the value of <math>Y</math> at time <math>t</math>, i.e., <math>Y(t)</math>, only depends on that of <math>X</math> at the same time, i.e., <math>X(t)</math>. Various estimation methods can be applied to model ({{EquationNote|6}}).<ref>{{Cite journal |last=Fan and|first=Jianqing |last2=Zhang (1999).|first2=Wenyang "|date= |title=Statistical estimation in varying coefficient models" |url=https://projecteuclid.org/journals/annals-of-statistics/volume-27/issue-5/Statistical-estimation-in-varying-coefficient-models/10.1214/aos/1017939139.full ''|journal=The Annals of Statistics''.'''|volume=27'''(|issue=5):1491–1518.[[Digital|pages=1491–1518 object identifier|doi]]:[http://doi.org/=10.1214/aos/1017939139 10.1214/aos/1017939139].|issn=0090-5364}}</ref><ref>Huang, Wu and Zhou (2004). "Polynomial spline estimation and inference for varying coefficient models with longitudinal data". ''Biometrika''. '''14''' (3):763–788. https://www.jstor.org/stable/24307415.</ref><ref>Şentürk and Müller (2010). "Functional varying coefficient models for longitudinal data". ''Journal of the American Statistical Association''. '''105''' (491):1256–1264. [[Digital object identifier|doi]]:[http://doi.org/10.1198/jasa.2010.tm09228 10.1198/jasa.2010.tm09228].</ref><br />
Adding multiple functional covariates, model ({{EquationNote|6}}) can also be extended to
