diff --git a/doc/NEWS.Rd b/doc/NEWS.Rd
index b4a953a5f5..48fbeaa341 100644
--- a/doc/NEWS.Rd
+++ b/doc/NEWS.Rd
@@ -349,6 +349,10 @@
       integer to double, analogously with \code{seq.default()},
       \code{seq.int()} and \code{seq.POSIXt()}, resolving a \emph{modified}
       \PR{18782}.
+
+      \item The parser now accepts hexadecimal constants with a decimal
+      point without an exponent (taken as \code{p0}) as documented in
+      \code{?NumericConstants} (\PR{18819}).
     }
   }
 }
diff --git a/src/main/gram.c b/src/main/gram.c
index 672d2f1e9e..03cd3ec438 100644
--- a/src/main/gram.c
+++ b/src/main/gram.c
@@ -70,7 +70,7 @@
 
 /*
  *  R : A Computer Language for Statistical Data Analysis
- *  Copyright (C) 1997--2023  The R Core Team
+ *  Copyright (C) 1997--2024  The R Core Team
  *  Copyright (C) 2009--2011  Romain Francois
  *  Copyright (C) 1995--1997  Robert Gentleman and Ross Ihaka
  *
@@ -4930,7 +4930,8 @@ static int NumericValue(int c)
 		    YYTEXT_PUSH(c, yyp);
 		if (nd == 0) return ERROR;
 	    }
-            if (seendot && !seenexp) return ERROR;
+// ?NumericComstants says exponent is optional (as does C99)
+//            if (seendot && !seenexp) return ERROR;
 	    if (c == 'L') /* for getParseData */
 	    {
 		// seenexp will be checked later
diff --git a/src/main/gram.y b/src/main/gram.y
index 85d96bd30e..884e470bba 100644
--- a/src/main/gram.y
+++ b/src/main/gram.y
@@ -2,7 +2,7 @@
 %{
 /*
  *  R : A Computer Language for Statistical Data Analysis
- *  Copyright (C) 1997--2023  The R Core Team
+ *  Copyright (C) 1997--2024  The R Core Team
  *  Copyright (C) 2009--2011  Romain Francois
  *  Copyright (C) 1995--1997  Robert Gentleman and Ross Ihaka
  *
@@ -2621,7 +2621,8 @@ static int NumericValue(int c)
 		    YYTEXT_PUSH(c, yyp);
 		if (nd == 0) return ERROR;
 	    }
-            if (seendot && !seenexp) return ERROR;
+// ?NumericComstants says exponent is optional (as does C99)
+//            if (seendot && !seenexp) return ERROR;
 	    if (c == 'L') /* for getParseData */
 	    {
 		// seenexp will be checked later
diff --git a/tests/reg-tests-1e.R b/tests/reg-tests-1e.R
index 6c61948cf0..e16d55cd03 100644
--- a/tests/reg-tests-1e.R
+++ b/tests/reg-tests-1e.R
@@ -1552,7 +1552,12 @@ for(x in list(x3 = {n <- 3L; x <- diag(n); x[n,n] <- 0; x},
 }
 ## kappa(..)  returned 1 or {0 with a warning} in R <= 4.4.2
 
-
+## hexadecimal contants with and without exponent.
+0x1.234p0
+0x1.234p7
+0x1.234p-7
+0x1.234
+## last was a (deliberate) parse error in R < 4.5.0, but not as documented.
 
 ## keep at end
 rbind(last =  proc.time() - .pt,