stacking columns into 1 column in R

I have a data frame that looks like:

ID Time U1 U2 U3 U4 ...
1  20    1  2 3  5 .. 
2  20    2  5 9  4 ..
3  20    2  5 6  4 ..
.
.

And I would need to keep it like: 

ID Time  U
1  20    1
1  20    2
1  20    3
1  20    5
2  20    2
2  20    5
2  20    9
2  20    4
3  20    2
3  20    5
3  20    6
3  20    4

I tried with:

X <- read.table("mydata.txt", header=TRUE, sep=",")
X_D <- as.data.frame(X)
X_new <- stack(X_D, select = -c(ID, Time))

But I haven't managed to get the data into that form. Honestly, I have little experience with stacking/transposing, so any help is greatly appreciated!