diff --git a/lib/matplotlib/contour.py b/lib/matplotlib/contour.py
@@ -701,7 +701,7 @@ def __init__(self, ax, *args,
                  hatches=(None,), alpha=None, origin=None, extent=None,
                  cmap=None, colors=None, norm=None, vmin=None, vmax=None,
                  extend='neither', antialiased=None, nchunk=0, locator=None,
-                 transform=None,
+                 transform=None, negative_linestyles=None,
                  **kwargs):
         """
         Draw contour lines or filled regions, depending on
@@ -786,6 +786,13 @@ def __init__(self, ax, *args,
 
         self._transform = transform
 
+        self.negative_linestyles = negative_linestyles
+        # If negative_linestyles was not defined as a kwarg,
+        # define negative_linestyles with rcParams
+        if self.negative_linestyles is None:
+            self.negative_linestyles = \
+                mpl.rcParams['contour.negative_linestyle']
+
         kwargs = self._process_args(*args, **kwargs)
         self._process_levels()
 
@@ -1276,11 +1283,10 @@ def _process_linestyles(self):
         if linestyles is None:
             tlinestyles = ['solid'] * Nlev
             if self.monochrome:
-                neg_ls = mpl.rcParams['contour.negative_linestyle']
                 eps = - (self.zmax - self.zmin) * 1e-15
                 for i, lev in enumerate(self.levels):
                     if lev < eps:
-                        tlinestyles[i] = neg_ls
+                        tlinestyles[i] = self.negative_linestyles
         else:
             if isinstance(linestyles, str):
                 tlinestyles = [linestyles] * Nlev
@@ -1751,6 +1757,18 @@ def _initialize_x_y(self, z):
     iterable is shorter than the number of contour levels
     it will be repeated as necessary.
 
+negative_linestyles : {*None*, 'solid', 'dashed', 'dashdot', 'dotted'}, \
+                       optional
+    *Only applies to* `.contour`.
+
+    If *negative_linestyles* is None, the default is 'dashed' for
+    negative contours.
+
+    *negative_linestyles* can also be an iterable of the above
+    strings specifying a set of linestyles to be used. If this
+    iterable is shorter than the number of contour levels
+    it will be repeated as necessary.
+
 hatches : list[str], optional
     *Only applies to* `.contourf`.
 

diff --git a/lib/matplotlib/tests/test_contour.py b/lib/matplotlib/tests/test_contour.py
@@ -605,3 +605,80 @@ def test_subfigure_clabel():
         CS = ax.contour(X, Y, Z)
         ax.clabel(CS, inline=True, fontsize=10)
         ax.set_title("Simplest default with labels")
+
+
+@pytest.mark.parametrize(
+    "style", ['solid', 'dashed', 'dashdot', 'dotted'])
+def test_linestyles(style):
+    delta = 0.025
+    x = np.arange(-3.0, 3.0, delta)
+    y = np.arange(-2.0, 2.0, delta)
+    X, Y = np.meshgrid(x, y)
+    Z1 = np.exp(-X**2 - Y**2)
+    Z2 = np.exp(-(X - 1)**2 - (Y - 1)**2)
+    Z = (Z1 - Z2) * 2
+
+    # Positive contour defaults to solid
+    fig1, ax1 = plt.subplots()
+    CS1 = ax1.contour(X, Y, Z, 6, colors='k')
+    ax1.clabel(CS1, fontsize=9, inline=True)
+    ax1.set_title('Single color - positive contours solid (default)')
+    assert CS1.linestyles is None  # default
+
+    # Change linestyles using linestyles kwarg
+    fig2, ax2 = plt.subplots()
+    CS2 = ax2.contour(X, Y, Z, 6, colors='k', linestyles=style)
+    ax2.clabel(CS2, fontsize=9, inline=True)
+    ax2.set_title(f'Single color - positive contours {style}')
+    assert CS2.linestyles == style
+
+    # Ensure linestyles do not change when negative_linestyles is defined
+    fig3, ax3 = plt.subplots()
+    CS3 = ax3.contour(X, Y, Z, 6, colors='k', linestyles=style,
+                      negative_linestyles='dashdot')
+    ax3.clabel(CS3, fontsize=9, inline=True)
+    ax3.set_title(f'Single color - positive contours {style}')
+    assert CS3.linestyles == style
+
+
+@pytest.mark.parametrize(
+    "style", ['solid', 'dashed', 'dashdot', 'dotted'])
+def test_negative_linestyles(style):
+    delta = 0.025
+    x = np.arange(-3.0, 3.0, delta)
+    y = np.arange(-2.0, 2.0, delta)
+    X, Y = np.meshgrid(x, y)
+    Z1 = np.exp(-X**2 - Y**2)
+    Z2 = np.exp(-(X - 1)**2 - (Y - 1)**2)
+    Z = (Z1 - Z2) * 2
+
+    # Negative contour defaults to dashed
+    fig1, ax1 = plt.subplots()
+    CS1 = ax1.contour(X, Y, Z, 6, colors='k')
+    ax1.clabel(CS1, fontsize=9, inline=True)
+    ax1.set_title('Single color - negative contours dashed (default)')
+    assert CS1.negative_linestyles == 'dashed'  # default
+
+    # Change negative_linestyles using rcParams
+    plt.rcParams['contour.negative_linestyle'] = style
+    fig2, ax2 = plt.subplots()
+    CS2 = ax2.contour(X, Y, Z, 6, colors='k')
+    ax2.clabel(CS2, fontsize=9, inline=True)
+    ax2.set_title(f'Single color - negative contours {style}'
+                   '(using rcParams)')
+    assert CS2.negative_linestyles == style
+
+    # Change negative_linestyles using negative_linestyles kwarg
+    fig3, ax3 = plt.subplots()
+    CS3 = ax3.contour(X, Y, Z, 6, colors='k', negative_linestyles=style)
+    ax3.clabel(CS3, fontsize=9, inline=True)
+    ax3.set_title(f'Single color - negative contours {style}')
+    assert CS3.negative_linestyles == style
+
+    # Ensure negative_linestyles do not change when linestyles is defined
+    fig4, ax4 = plt.subplots()
+    CS4 = ax4.contour(X, Y, Z, 6, colors='k', linestyles='dashdot',
+                      negative_linestyles=style)
+    ax4.clabel(CS4, fontsize=9, inline=True)
+    ax4.set_title(f'Single color - negative contours {style}')
+    assert CS4.negative_linestyles == style