I think you need to provide more information. One option is bootstrapping (but that can be tricky in a repeated measures model). Why do you think a parametric model would not work? What is your sample size and what is the distribution of your outcome (Y) variable? Are there still problems when you look at the residuals of the model? (Generally a conventional regression model just assumes normality of the residuals).

Alternatives (apart from bootstrapping) include transformations, generalised linear models and some related approaches.

Hello Thom,

Thank you for your response. I usually check the normality of my data distribution first. In this case I have different treatment groups, which I check individually. Please refer to the data in the attachment (Phe.pdf). There are 3 timepoints and with different sample sizes for each time point (n=6, n=4 and n=6 again)

For these reasons I thought of directly using a non-parametric version. But you are right I should check for the residuals and hence, I did and the plots are attached for your reference. What do you make of this?

They look OK to me. You have one extreme, high influence value, but otherwise it does not look unsuitable for ANOVA or regression.

Any reason you don't include an interaction term:

lm(value ~ factor(time) * condition)

or 

lm(value ~ scale(time, scale=FALSE) * condition)

The latter model centres time to improve interpretation of the interaction. The former is the ANOVA parameterisation.