Seems they are pretty much interchangeable. I can't think of a time to use one that I could not use the other. . I deny answering the question well. I deny having answered the question well. . I flatly deny being involved. I flatly deny having been involved. . The "having done" has a sense of something completed in the past. If you can think of a way that this is important, then you have a difference. . I deny doing the drawing. - a continuing action, in that it was not instantaneous. I deny having done the drawing. - This "doing" is not completed. No sense of the dooing taking time. .