OK,
Thanks for all hints.
Stepper needs to run from 240 to around 1000 rpm.
It is a 200 steps 3 A version motor currently running full steps.
240 rpm is 800 steps if I am correct.
No need to synchronize with anything else. Just run Forest Gump, just run 
I can life with a 1 second interval Serial.print in this case of this project for sending data to the PC.
I tested Serial.begin at 115200 with this test code and that works fine........but
#include <AccelStepper.h>
#include <MultiStepper.h>
// debug code for steppermotor using serial monitor
// the control is done by an Arduino Nano board in conjunction with a TBS6050 stepperboard.
// set to 3 amp
// 200 steps per rotation
AccelStepper stepper(1, 9, 10); // step-dir set up the stepper as 4 wire bipolair on pin 9,10 for TB6560 DRIVER or other driver board
boolean StepPin = 9; // output
boolean DirPin = 10; // output
boolean MotorPin = 11; //output
void setup()
{
Serial.begin(115200);
//*******************
pinMode(StepPin, OUTPUT);
pinMode(DirPin, OUTPUT);
pinMode(MotorPin, OUTPUT);
//*******************
digitalWrite(StepPin, LOW);
digitalWrite(DirPin, LOW);
digitalWrite(MotorPin, LOW);
//*******************
digitalWrite(DirPin, LOW); //change this if direction is wrong
stepper.setMaxSpeed(1200);
}
void loop()
{
digitalWrite(StepPin, LOW);
digitalWrite(DirPin, LOW);
stepper.setSpeed(800); // 240 prm 1/1 steps
stepper.runSpeed();
Serial.print(123456");
} // end void loop
as soon as I add
Serial.print(12);
Serial.println(12);
I am back where I started..
I know Serial.print cost speed.
I read a loadcell and one infrared MLX90614 temperature sensor that need to be ported to the PC. So I need the Serial.print.
So serial.print is like this
Serial.print ("A,");
Serial.println (ValueOut1); // weigth 6 digits
Serial.print ("B,");
Serial.println(mlx.readObjectTempC(), 0); // two digits
Serial.print ("C,");
Serial.println(mlx.readAmbientTempC(), 0); // two digits
Basic as the word, not in the code lanquage 
Paco