diff --git a/kivy/data/style.kv b/kivy/data/style.kv
index 9a1e35faf..63aa14ff6 100644
--- a/kivy/data/style.kv
+++ b/kivy/data/style.kv
@@ -713,12 +713,12 @@
 <ScrollView>:
     canvas.after:
         Color:
-            rgba: self.bar_color[:3] + [self.bar_color[3] * self.bar_alpha if self.do_scroll_y else 0]
+            rgba: self.bar_color[:3] + [self.bar_color[3] * self.bar_alpha if (self.do_scroll_y and self.viewport_size[1]>self.height) else 0]
         Rectangle:
             pos: self.right - self.bar_width - self.bar_margin, self.y + self.height * self.vbar[0]
             size: self.bar_width, self.height * self.vbar[1]
         Color:
-            rgba: self.bar_color[:3] + [self.bar_color[3] * self.bar_alpha if self.do_scroll_x else 0]
+            rgba: self.bar_color[:3] + [self.bar_color[3] * self.bar_alpha if (self.do_scroll_x and self.viewport_size[0] > self.width) else 0]
         Rectangle:
             pos: self.x + self.width * self.hbar[0], self.y + self.bar_margin
             size: self.width * self.hbar[1], self.bar_width