they can. when we are talking about parallel, it can be concluded into 2 situations, the parallel of straight lines and the parallel of curves. the situation of straight lines is just a particular example of paralle.
there are many example of parallel of curves, for example, concentric circles, tortuous railway and so on. the essential character of parallel is a certain unchange distance, the concentric circles is a good example of this. at the same time circles are also curves. so curves can be parallel to each other.