Does GAM (Generalized Additive Model) have collinearity problem? There is collinearity effect in linear regression methods. For example, this question is about collinear predictors in GLM.
But GAMs are nonlinear, do we need to check the collinearity of independent variables before using GAMs?
 A: GAM models can be afflicted by concurvity (the extension of GLM collinearity to GAM models). 
According to https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/concurvity.html:
"Concurvity occurs when some smooth term in a model could be approximated by     
one or more of the other smooth terms in the model. This is often the case     
when a smooth of space is included in a model, along with smooths of other      
covariates that also vary more or less smoothly in space. Similarly it tends   
to be an issue in models including a smooth of time, along with smooths of 
other time varying covariates.

Concurvity can be viewed as a generalization of co-linearity, and causes   
similar problems of interpretation. It can also make estimates somewhat 
unstable (so that they become sensitive to apparently innocuous modelling   
details, for example)."

The above link explains how you can compute three different measures of concurvity for a GAM model fitted with the mgcv package in R, all of which are bounded between 0 and 1 (with 0 indicating no concurvity). 
Thus, you do have to check for the potential presence of concurvity in your GAM models by computing appropriate measures of concurvity and making sure they are not too high (i.e., not too close to 1). See also gam smoother vs parametric term (concurvity difference), https://jroy042.github.io/nonlinear/week3.html and https://eric-pedersen.github.io/mgcv-esa-workshop/slides/02-model_checking.html#/. 
