diff --git a/arch/um/sys-i386/ptrace.c b/arch/um/sys-i386/ptrace.c
index e839ce6..8032a10 100644
--- a/arch/um/sys-i386/ptrace.c
+++ b/arch/um/sys-i386/ptrace.c
@@ -6,6 +6,7 @@
 #include <linux/config.h>
 #include <linux/compiler.h>
 #include "linux/sched.h"
+#include "linux/mm.h"
 #include "asm/elf.h"
 #include "asm/ptrace.h"
 #include "asm/uaccess.h"
@@ -26,9 +27,17 @@
 
 	n = copy_from_user(&instr, (void __user *) addr, sizeof(instr));
 	if(n){
-		printk("is_syscall : failed to read instruction from 0x%lx\n",
-		       addr);
-		return(0);
+		/* access_process_vm() grants access to vsyscall and stub,
+		 * while copy_from_user doesn't. Maybe access_process_vm is
+		 * slow, but that doesn't matter, since it will be called only
+		 * in case of singlestepping, if copy_from_user failed.
+		 */
+		n = access_process_vm(current, addr, &instr, sizeof(instr), 0);
+		if(n != sizeof(instr)) {
+			printk("is_syscall : failed to read instruction from "
+			       "0x%lx\n", addr);
+			return(1);
+		}
 	}
 	/* int 0x80 or sysenter */
 	return((instr == 0x80cd) || (instr == 0x340f));
diff --git a/arch/um/sys-x86_64/ptrace.c b/arch/um/sys-x86_64/ptrace.c
index 74eee5c..147bbf0 100644
--- a/arch/um/sys-x86_64/ptrace.c
+++ b/arch/um/sys-x86_64/ptrace.c
@@ -8,6 +8,7 @@
 #include <asm/ptrace.h>
 #include <linux/sched.h>
 #include <linux/errno.h>
+#include <linux/mm.h>
 #include <asm/uaccess.h>
 #include <asm/elf.h>
 
@@ -136,9 +137,28 @@
 */
 }
 
+/* XXX Mostly copied from sys-i386 */
 int is_syscall(unsigned long addr)
 {
-	panic("is_syscall");
+	unsigned short instr;
+	int n;
+
+	n = copy_from_user(&instr, (void __user *) addr, sizeof(instr));
+	if(n){
+		/* access_process_vm() grants access to vsyscall and stub,
+		 * while copy_from_user doesn't. Maybe access_process_vm is
+		 * slow, but that doesn't matter, since it will be called only
+		 * in case of singlestepping, if copy_from_user failed.
+		 */
+		n = access_process_vm(current, addr, &instr, sizeof(instr), 0);
+		if(n != sizeof(instr)) {
+			printk("is_syscall : failed to read instruction from "
+			       "0x%lx\n", addr);
+			return(1);
+		}
+	}
+	/* sysenter */
+	return(instr == 0x050f);
 }
 
 int dump_fpu(struct pt_regs *regs, elf_fpregset_t *fpu )